Pajek manual - Vladimir Batagelj

Pajek 

Program for Analysis and 

Visualization of Large Networks 

Reference Manual 

List of commands with short explanation 

version 2.05 

Vladimir Batagelj and Andrej Mrvar 

Ljubljana, September 24, 2011

c○1996, 2011 V. Batagelj, A. Mrvar. Free for noncommercial use. 

PdfLaTex version October 1, 2003 

Vladimir Batagelj 

Department of Mathematics, FMF 

University of Ljubljana, Slovenia 

http://vlado.fmf.uni-lj.si/ 

vladimir.batagelj@fmf.uni-lj.si 

Andrej Mrvar 

Faculty of Social Sciences 

University of Ljubljana, Slovenia 

http://mrvar.fdv.uni-lj.si/ 

andrej.mrvar@fdv.uni-lj.si

Contents 

1 Pajek 3 

2 Data objects 6 

3 Main Window Tools 8 

3.1 File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

3.2 Net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

3.3 Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

3.4 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 

3.5 Partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 

3.6 Partitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 

3.7 Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 

3.8 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 

3.9 Permutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 

3.10 Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 

3.11 Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 

3.12 Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 

3.13 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 

3.14 Info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 

3.15 Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 

4 Draw Window Tools 56 

4.1 Main Window Draw Tool . . . . . . . . . . . . . . . . . . . . . . 56 

4.2 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 

4.3 Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 

4.4 GraphOnly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

4.5 Previous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

4.6 Redraw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

4.7 Next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

4.8 ZoomOut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

4.9 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

4.10 Export . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 

4.11 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 

4.12 Move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 

4.13 Info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

5 Exports to EPS/SVG/X3D/VRML 69 

5.1 Defaults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 

5.2 Parameters in EPS, SVG, X3D, and VRML Defaults Window . . . 69 

1

5.3 Exporting pictures to EPS/SVG – defining parameters in input file 73 

5.4 Using Unicode in Pajek’s pictures . . . . . . . . . . . . . . . . . 77 

6 Using Macros in Pajek 80 

6.1 What is a Macro? . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

6.2 How to record a Macro? . . . . . . . . . . . . . . . . . . . . . . 80 

6.3 How to execute the Macro? . . . . . . . . . . . . . . . . . . . . . 80 

6.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

6.5 List of macros available in installation file . . . . . . . . . . . . . 81 

6.5.1 Macros prepared for genealogies and other acyclic networks 81 

6.5.2 Macros prepared for computing derived kinship relations . 82 

6.6 Repeating last command . . . . . . . . . . . . . . . . . . . . . . 82 

7 Blockmodeling in Pajek 84 

7.1 MDL files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 

7.2 Examples of MDL files . . . . . . . . . . . . . . . . . . . . . . . 86 

7.2.1 Regular blocks . . . . . . . . . . . . . . . . . . . . . . . 86 

7.2.2 Diagonal blocks (clustering) . . . . . . . . . . . . . . . . 86 

7.2.3 Acyclic model (up) . . . . . . . . . . . . . . . . . . . . . 86 

7.2.4 Acyclic model with symmetric clusters (down) . . . . . . 86 

7.2.5 Center-Periphery . . . . . . . . . . . . . . . . . . . . . . 87 

7.2.6 Regular path . . . . . . . . . . . . . . . . . . . . . . . . 87 

7.2.7 Regular chain . . . . . . . . . . . . . . . . . . . . . . . . 87 

7.2.8 2-mode ’standard model’ for Davis.net . . . . . . . . . . 88 

8 Colors in Pajek 89 

9 Citing Pajek 91 

2

Pajek– Manual 3 

1 Pajek 

Pajek is a program, for Windows, for analysis and visualization 

of large networks having some thousands or even 

millions of vertices. In Slovenian language the word pajek 

means spider. The latest version of Pajek is freely 

available, for noncommercial use, at its home page: 

http://vlado.fmf.uni-lj.si/pub/networks/pajek/ 

We started the development of Pajek in November 1996. Pajek is implemented 

in Delphi (Pascal). Some procedures were contributed by Matjaˇz Zaverˇsnik. 

The main motivation for development of Pajek was the observation that 

there exist several sources of large networks that are already in machine-readable 

form. Pajek should provide tools for analysis and visualization of such networks: 

collaboration networks, organic molecule in chemistry, protein-receptor 

interaction networks, genealogies, Internet networks, citation networks, diffusion 

(AIDS, news, innovations) networks, data-mining (2-mode networks), etc. See 

also collection of large networks at: 

http://vlado.fmf.uni-lj.si/pub/networks/data/ 

The design of Pajek is based on our previous experiences gained in development 

of graph data structure and algorithms libraries Graph and X-graph, collection 

of network analysis and visualization programs STRAN, RelCalc, Draw, 

Energ, and SGML-based graph description markup language NetML. 

http://vlado.fmf.uni-lj.si/pub/networks/default.htm 

Figure 1: Pajek/Spider 

V. Batagelj and A. Mrvar Pajek 2.05 / September 24, 2011

4 Pajek– Manual 

cut-out 

local 

context 

global 

inter-links 

hierarchy 

reduction 

Figure 2: Approaches to deal with large networks 

The main goals in the design of Pajek are: 

• to support abstraction by (recursive) decomposition of a large network into 

several smaller networks that can be treated further using more sophisticated 

methods; 

• to provide the user with some powerful visualization tools; 

• to implement a selection of efficient (subquadratic) algorithms for analysis 

of large networks. 

With Pajek we can: find clusters (components, neighbourhoods of ‘important’ 

vertices, cores, etc.) in a network, extract vertices that belong to the same 

clusters and show them separately, possibly with the parts of the context (detailed 

local view), shrink vertices in clusters and show relations among clusters (global 

view). 

Besides ordinary (directed, undirected, mixed) networks Pajek supports also 

multi-relational networks, 2-mode networks (bipartite (valued) graphs – networks 

between two disjoint sets of vertices), and temporal networks (dynamic graphs – 

networks changing over time). 



Figure 3: Pajek textbook 

This manual provides short explanations of all procedures implemented in the 

last version of Pajek. The novice users we advise to read the Pajek textbook 

[31] 

de Nooy W., Mrvar A., Batagelj V. (2002) Exploratory Social Network 

Analysis With Pajek. Structural Analysis in the Social Sciences 

27, Cambridge University Press, 2005. 

For an overview of network analysis with Pajek see the NICTA workshop slides 

[5]. 



2 Data objects 

In Pajek six types of objects are used: 

Figure 4: Pajek’s Main Window 

1. Networks – main objects (vertices and lines). Default extension: .net. 

Network can be presented on input file in different ways: 

• using arcs/edges (e.g. 1 2 – line from 1 to 2) 

• using arcslists/edgeslists (e.g. 1 2 3 – line from 1 to 2 and from 1 to 3) 

• matrix format 

• UCINET, GEDCOM, chemical formats. . . 

Additional information for network drawing can be included in input file as 

well. This is explained in the section Exports to EPS/SVG/VRML. 

2. Partitions – they tell for each vertex to which class vertex belong. Default 

extension: .clu. 

3. Permutations – reordering of vertices. Default extension: .per. 

4. Clusters – subset of vertices (e.g. one class from partition). Default extension: 

.cls. 

5. Hierarchies – hierarchically ordered vertices. Example: 

Root 

g1 g2 

g11 g12 v5,v6,v7 

v1,v2 v3,v4 



Root has two subgroups – g1 and g2. g2 is a leaf – cluster with vertices 

v5,v6 and v7. g1 has two subgroups – g11 and g12. . . Default extension: 

.hie. 

6. Vectors – they tell for each vertex some numerical property (real number). 

Default extension: .vec. 

By double clicking on selected network, partition,... you can show the object 

on screen. 

The procedures in Pajek’s main window (see Figure 4) are organized according 

to the types of data objects they use as input. 

Permutations, partitions and vectors can be used to store properties of vertices 

measured in different scales: ordered, nominal (categorical) and numeric. 

Figure 5: Spider web; Photo: Vladimir Batagelj. 



3 Main Window Tools 

3.1 File 

Input/Output manipulation with the six data objects. 

• Network – N 

– Read – Read network from Ascii file. 

– Edit – Edit network. Choose vertex, show its neighbors and then: 

∗ add new lines to/from selected vertex (by left mouse double clicking 

on Newline); 

∗ delete lines (by left mouse double clicking); 

∗ change value of line (by single right mouse clicking); 

∗ subdivide line to two orthogonal lines using new invisible vertex 

(by single middle mouse clicking). 

– Save – Save selected network to Ascii file. 

If network represents Ore graph with the following five relations (arcs): 

1. Wi→Hu, 2. Mo→Da, 3. Mo→So, 4. Fa→Da, 5. Fa→So 

it can be stored as GEDCOM file. 

The other possibility is Pajek Ore graph: 1.Fa→Ch, 2.Mo→Ch, 3.Hu- 

Wi (edge), or 1.Pa→Ch, 3.Hu-Wi (edge). 

– Export Matrix to EPS – write matrix in EPS format: 

∗ Original – using default numbering (for 1-mode and 2-mode networks). 

∗ Using Permutation – using current permutation. Additionally 

lines can be drawn to divide different classes defined by selected 

partition. Option can be used for 1-mode and 2-mode networks. 

∗ Using Partition – using current partition. In the text window 

number and density of lines among classes (and vertices in selected 

two classes) are displayed. Additionally matrix is exported 

to EPS where density is expressed using shadowing: 

1. Structural – Densities are normalized according to maximum 

possible number of lines among classes (suitable for 

dense networks). 

2. Delta – Densities are normalized according to vertices having 

the highest number of input and output neighbors in classes 

(suitable for sparse networks). 


Pajek – Manual 9 

∗ Diamonds for Negative Values, Circles for 0 – Squares are used 

for posititive values, diamonds for negative and circles for value 

0 (useful for black and white printing). 

∗ Diamonds, Circles and Lines in GreyScale – Diamonds, circles 

and dividing lines are drawn in greyscale (not in red, green and 

blue). 

∗ Labels on Top/Right – Labels are written on the top and on the 

right of the matrix - suitable for longer labels. 

∗ Only Black Borders – All squares in matrix have black borders, 

otherwise dark squares will have white and light squares will have 

black borders. 

∗ Thick Boundary Line – Use thicker line for dividing clusters. 

∗ Large Squares/Diamonds/Circles – Use larger or smaller squares, 

diamonds, and circles. 

∗ Use Partition Colors for Vertex Labels – Labels of vertices are 

displayed using partition colors. 

– Change Label of selected network. 

– Dispose selected network from memory. 

• Time Events Network – N 

– Read Time Events – Read time network described using time events. 

See Table 1. 

List of properties s can be empty as well. If several edges (arcs) can 

connect two vertices, additional tag like :k (k-th line) must be given to 

determine to which line the command applies. E.g. command HE:3 

14 37 results in hiding the third edge connecting vertices 14 and 37. 

Example of time network described using time events: 

*Vertices 3 

*Events 

TI 1 

AV 2 "b" 

TE 3 

HV 2 

TI 4 

AV 3 "e" 

TI 5 

AV 1 "a" 

TI 6 

AE 1 3 1 

TI 7 

SV 2 

AE 1 2 1 


10 Pajek – Manual 

Table 1: List of time events. 

Event Explanation 

TI t initial events – following events happen when 

time point t starts 

TE t end events – following events happen when 

time point t is finished 

AV vns add vertex v with label n and properties s 

HV v hide vertex v 

SV v show vertex v 

DV v delete vertex v 

AA uvs add arc (u,v) with properties s 

HA uv hide arc (u,v) 

SA uv show arc (u,v) 

DA uv delete arc (u,v) 

AE uvs add edge (u:v) with properties s 

HE uv hide edge (u:v) 

SE uv show edge (u:v) 

DE uv delete edge (u:v) 

CV vs change vertex property – change property of vertex v to s 

CA uvs change arc property – change property of arc (u,v) to s 

CE uvs change edge property – change property of edge (u:v) to s 

CT uv change type – change (un)directedness of line (u,v) 

CD uv change direction of arc (u,v) 

PE uvs replace pair of arcs (u,v) and (v,u) by single edge (u:v) 

with properties s 

AP uvs add pair of arcs (u,v) and (v,u) 


DP uv delete pair of arcs (u,v) and (v,u) 

EP uvs replace edge (u:v) by pair of arcs (u,v) and (v,u) 




TE 7 

DE 1 2 

DV 2 

TE 8 

DE 1 3 

TE 10 

HV 1 

TI 12 

SV 1 

TE 14 

DV 1 

See also other possibility: description of time network using time intervals. 

– Save – Save time network in time events format. 

• Partition – C 

– Read partition from Ascii file. 

– Edit partition (put vertices to classes). 

– Save selected partition to Ascii file. 

– Change Label of selected partition. 

– Dispose selected partition from memory. 

• Permutation – P 

– Read permutation from Ascii file. 

– Edit permutation (interchange positions of two vertices). 

– Save selected permutation to Ascii file. 

– Change Label of selected permutation. 

– Dispose selected permutation from memory. 

• Cluster – S (list of selected vertices) 

– Read cluster from Ascii file. 

– Edit cluster (add and delete vertices). 

– Save selected cluster to Ascii file. 

– Change Label of selected cluster. 

– Dispose selected cluster from memory. 

• Hierarchy – H 

– Read hierarchy from Ascii file. 



– Edit hierarchy (change types and names of nodes, or show vertices 

(and subtree) belonging to selected node). Nodes can be pushed up 

and down within hierarcy. 

– Save selected hierarchy to Ascii file. 

– Change Label of selected hierarchy. 

– Dispose selected hierarchy from memory. 

• Vector – V 

– Read vector from Ascii file. 

– Edit vector (change components of vector). 

– Save selected vector(s) to Ascii file. If cluster representing vector id’s 

is present, all vectors with corresponding id numbers will be saved to 

the same output file. Vector’s id can be added to cluster by pressing 

V on the selected vector (empty cluster should be created first). All 

vectors must have the same dimensions. 

– Change Label of selected vector. 

– Dispose selected vector from memory. 

• Pajek Project File – *.paj 

– Read Pajek project file (file containing all possible Pajek data objects 

– networks, partitions, permutations, clusters, hierarchies and 

vectors). 

– Save all currently loaded objects as a Pajek project file. 

• Repeat session – During program execution all commands are written to 

file *.log. In this way you can repeat any execution by running selected 

log file. If you change in the log file a name of a file to ?, program will 

ask for name when running logfile next time (so you can repeat the same 

sequence of steps – logfile with different input data). If startup logfile (Pajek.log) 

exists (in the same directory as Pajek.exe), it is automatically executed 

every time when Pajek is run. 

• Show Report Window – Bring the report window in the front in the case 

that it was closed or is not visible. 

• Exit program. 



3.2 Net 

Operations, for which only a network is needed as input. 

• Transform 

– Transpose – Transposed network of selected network: 

∗ 1-Mode - Change direction of arrows. 

∗ 2-Mode - Interchange Rows and Cols. 

– Remove 

∗ Selected Vertices – Remove selected vertices from network. 

∗ all Edges – Remove all edges from selected network. 

∗ all Arcs – Remove all arcs from selected network. 

∗ Multiple Lines – Remove all multiple lines from selected network. 

1. Sum Values – Values of all deleted lines are added to not 

deleted line between corresponding two vertices. 

2. Number of Lines – Value of line between two vertices in a 

new network correspond to the number of lines between the 

two vertices in original network. 

3. Min Value – Minimum value of all lines between two vertices 

is selected. 

4. Max Value – Maximum value of all lines between two vertices 

is selected. 

5. Single Line – Value of line between two vertices in a new 

network is 1. 

∗ Loops – Remove all loops from selected network. 

∗ Lines with Value 

1. lower than – Remove all lines with value lower than specified 

value. 

2. higher than – Remove all lines with value higher than specified 

value. 

3. within interval – Remove all lines with values within specified 

interval. 

∗ all Arcs from each Vertex except 

1. k with Lowest Line Values – Sort lines around vertices in 

ascending order according to output line values. Keep only 

selected number of lines with lowest values. 



2. k with Highest Line Values – Sort lines around vertices in 

descending order according to output line values. Keep only 

selected number of lines with highest values. 

3. keep Lines with Value equal to the k-th Value – Determine 

what to do with lines with value equal to the k-th value (remove 

them or not). 

∗ Triangle – Remove arcs belonging to lower or upper triangle. 

– Add additional vertices, lines or vertices/lines labels to network. 

∗ Vertices – Copy network to new network. Dimension can be enlarged 

for selected number of vertices (additional vertices without 

lines are added). 

∗ Source and Sink – If network is acyclic, add unique first and last 

vertex (new network has two artificial vertices). 

∗ Default Vertex Labels – Replace current labels of vertices by 

default vertices labels (v1, v2...). 

∗ Vertex Labels from File – Replace the default vertices labels (v1, 

v2...) by labels given in a file. 

∗ Line Labels as Line Values – replace labels of lines (or create 

new if there are no) with line values. Number of decimal places 

is the same as used in Draw window for marking lines with line 

values. 

∗ Sibling edges – Add sibling edges to vertices with a common 

1. Input – arc-ancestor 

2. Output – arc-descendant 

– Edges → Arcs – Convert all edges to arcs (in both directions) (make 

directed network). 

– Arcs → Edges 

∗ All – Convert all arcs to edges (make undirected network). 

∗ Bidirected only – Convert only arcs in both directions to edges: 

1. Sum Values – Value of the new edge is the sum of values of 

both arcs. 

2. Min Value – Value of the new edge is the smaller of values 

of arcs. 

3. Max Value – Value of the new edge is the larger of values of 

arcs. 

– Bidirected Arcs → Arc 



∗ Select Min Value – If there exist bidirected arcs between two 

vertices retain only the arc with lower value and remove the arc 

with higher value. If both values are equal replace both arcs with 

an edge. 

∗ Select Max Value – If there exist bidirected arcs between two 

vertices retain only the arc with higher value and remove the arc 

with lower value. If both values are equal replace both arcs with 

an edge. 

– Line Values – Transformations of line values: 

∗ Recode – Display frequency distribution of line values according 

to selected intervals and recode line values in this way. 

∗ Multiply by a constant. 

∗ Add Constant to line values. 

∗ Constant – min or max of line value and selected constant. 

∗ Absolute line values. 

∗ Absolute + Sqrt – square root of line values. 

∗ Truncate – truncated line values. 

∗ Exp – exponent of line values. 

∗ Ln – natural logarithm of line values. 

∗ Power – selected power of line values. 

∗ Normalize 

– Reduction 

1. Sum – normalize so that the sum of line values will be 1 

2. Max – normalize so that the maximum line value will be 1 

∗ Degree – (Recursively) delete from network all vertices with degree 

lower than selected value (according to Input, Output or All 

degree). Operation can be limited to selected cluster. 

∗ Hierarchical – Recursively delete from network all vertices that 

have only 0 or 1 neighbor. Results: simpler network and hierarchy 

with deleted vertices. Original network can be later restored (if we 

forget directions of lines). 

∗ Subdivisions – Recursively delete from network all vertices that 

have exactly 2 neighbors (together with corresponding two lines) 

and (instead of that) add direct line between these two neighbors. 

Result is simpler network (for drawing). Original network cannot 

be restored! 


16 Pajek – Manual 

Figure 6: Part of Reuters Terror News network on the 36th day. 

∗ Design (flow graph) Reduction of all structural parts of network 

according to McCabe (for programs – flow graphs) [50]. 

– Generate in Time – Generate network in specified time(s) or interval. 

Input first time, last time and step (integers). 

Additional parameters when vertices and lines are active should be 

given in network to perform this operation. They must be given between 

signs [ and ]: 

- is used to divide lower and upper limit of interval, 

, is used to separate intervals, 

* means infinity. Example: 

*Vertices 3 

1 "a" [5-10,12-14] 

2 "b" [1-3,7] 

3 "e" [4-*] 

*Edges 

1 2 1 [7] 



1 3 1 [6-8] 

Vertex ’a’ is active from times 5 to 10, and 12 to 14, vertex ’b’ in times 

1 to 3 and in time 7, vertex ’e’ from time 4 on. Line from 1 to 2 is active 

only in time 7, line from 1 to 3 in times 6 to 8. 

The lines and vertices in a temporal network should satisfy the consistency 

condition: if a line is active in time t then also its end-vertices 

are active in time t. When generating time slices of a given temporal 

network only ’consistent’ lines are generated. 

Note that time records should always be written as last in the row 

where vertices / lines are defined. 

See also other possibility of describing time network: description of 

time network using time events. 

∗ All – Generate all networks in specified times. 

∗ Only Different – Generate network in specified time only if the 

new network will differ in at least one vertex or line from the last 

network which was generated. 

∗ Interval – Generate network with vertices and lines present in 

selected interval. 

– 1-Mode to 2-Mode – Generate 2-mode network from any network. 

– 2-Mode to 1-Mode – Generate an ordinary (1-mode) network from 

2-mode (affiliation) network. Result is a valued network. To store 

a 2-mode network in input file use Pajek or Ucinet format (look at 

Davis.dat from Ucinet dataset). 

∗ Rows – Result is a network with relations among row elements 

(actors). The value of line tells number of common events of the 

two actors. 

∗ Columns – Result is network with relations among column elements 

(events). The value of a line tells number of actors that took 

part in both events. 

∗ Include Loops – If checked, loops with value telling the total 

number of events for each actor (total number of actors for each 

event), are added. 

∗ Multiple Lines – Generate nonvalued 1-mode network, where 

multiple lines among vertices can exist. The label of the generated 

line corresponds to the label of the event/actor that served 

to induce the line. If partition of the same dimension is present, 

multirelational network can be generated. 



∗ Normalize 1-Mode – Normalize the obtained 1-Mode network. 

1-Mode network must be obtained with option include loops checked, 

and multiple lines not checked: 

Geoij = 

Input ij = aij 

aij 

√ aiiajj 

ajj 

Output ij = aij 

Minij = 

Maxij = 

MinDirij = 

MaxDirij = 

aii 

aij 

min(aii, ajj) 

aij 

max(aii, ajj) 

� aij 

aii ≤ ajj 

aii 

0 otherwise 

� aij 

ajj 

aii ≤ ajj 

0 otherwise 

The obtained network is usually not sparse. To make it sparser 

use Net/Transform/Remove/lines with value/lower than. 

∗ Rows=Cols – Transform 2-Mode network with the same subsets 

of vertices to 1-Mode network. 

∗ Cols=0 – Transform 2-Mode network to 1-Mode network by setting 

number of columns to 0. The result is the same as changing 

for example *Vertices 32 18 to *Vertices 32 in input 

network file. 

– Multiple Relations 

∗ Extract Relation(s) – Extract one or selected list of relations 

from selected multiple relations network. 

∗ Canonical Numbering – Enumerate relations with sequential numbers 

1, 2,. . . 

∗ Generate 3-Mode Network – generate a 3-mode network from 

1-mode or 2-mode multirelational network. For each line in multirelational 

network r: i j v (line from i to j with value v, 

relation number is r) generate the following three lines (triangle): 

· 1-mode networks: 

i N+j v 



i 2N+r v 

N+j 2N+r v 

· 2-mode networks: 

i j v 

i N+M+r v 

j N+M+r v 

where N is cardinality of the first mode and M cardinality of the 

second mode. 

∗ Line Values − > Relation Numbers – Store line values as relation 

numbers (absolute truncated values). 

∗ Relation Numbers − > Line Values – Store relation numbers as 

line values. 

∗ Change Relation Number - Label – Change selected relation 

number to new relation number with corresponding label. 

– Sort Lines – 

∗ Neighbors around Vertices – For each vertex sort lines connected 

to it in ascending order according to other end-vertex. 

∗ Line Values – Sort lines in ascending or descending order according 

to line values. 

• Random Network – Generate random network of selected dimension 

– Total No. of Arcs – Generate random directed network of selected 

dimension and given number of arcs. 

– Vertices Output Degree – Generate random directed network of selected 

dimension and output degree of each vertex in given range. 

– Bernoulli/Poisson – Generate undirected, directed, acyclic, bipartite 

or 2-mode random network according to model defined by Bernoulli 

/ Poisson: each line is selected with the given probability p. Instead 

of p, which is for large and sparse networks (very) small number, in 

Pajek a more intuitive average degree d is used. They are connected 

with relations d = 1 � 

n v∈V deg(v) = 2m and m = pM where n = |V |, 

n 

m = |L| and M is the number of lines in maximal possible network – 

for example, for undirected graphs M = n(n − 1). 

– Scale Free – Generate scale free undirected, directed or acyclic network. 

The procedure is based on a refinement of the model for generating 

scale free networks, proposed in [55]. At each step of the growth 

a new vertex and k edges are added to the network N. The endpoints 



of the edges are randomly selected among all vertices according to the 

probability 

Pr(v) = α indeg(v) 

|E| 

+ β outdeg(v) 

|E| 

+ γ 1 

|V | 

where α + β + γ = 1. It is easy to check that � 

v∈V Pr(v) = 1. 

– Small World – Generate Small world random network. See [12]. 

– Extended Model – Generate random network according to extended 

model defined by Albert and Barabasi [3]. 

• Partitions – Partitioning Network. Result is a Partition. 

– Degree 

∗ Input – Number of lines into vertices. 

∗ Output – Number of lines out of vertices. 

∗ All – Number of neighbors of vertices. 

– Domain – For each vertex compute its domain according to input, 

output or all neighbors. Results are: 

∗ Partition containing size of domain - number of reachable vertices. 

∗ Vector containing the normalized size of domain - normalization 

is done by total number of vertices – 1. 

∗ Vector containing the average distance from/to domain. 

Proximity Prestige index can be computed by dividing the normalized 

size of domain by average distance. 

– Core – k-core is a subnetwork of given network where each vertex has 

at least k neighbors in the same core according to: 

∗ Input ... lines coming into vertex. 

∗ Output ... lines going out of vertex. 

∗ All ... all neighbors. 

∗ 2-Mode – core partition of a 2-mode network. Given minimum 

degree in first (k1) and minimum degree in second subset (k2) 

a new partition is generated where 0 means that vertex does not 

belong to the core of prespecified k1 and k2, 1 means that vertex 

belongs to that core. 



4957349 

4630896 

3891307 

4387039 

4583826 

4387038 

4510069 

4154697 

4349452 

4202791 

4558151 

4368135 

4293434 4290905 4361494 

4302352 4330426 

4195916 

4877547 

4770503 4795579 4797228 

4659502 

4526704 

4419263 4422951 

4621901 

4550981 

4502974 

4460770 4480117 4472293 4472592 

4340498 

4149413 

4113647 4130502 4032470 4083797 4082428 4118335 

4013582 4029595 4077260 4017416 

4415470 

4752414 

4709030 4719032 

4695131 4710315 4713197 4704227 

4514044 

4455443 

4400293 

4229315 4261652 

3954653 3947375 

3960752 

4198130 

4456712 

5555116 

5124824 5171469 5283677 

5016988 5122295 

5016989 

4820839 4832462 

4721367 

4657695 

4386007 

4357078 

3975286 4011173 4000084 

3876286 

3697150 3636168 3767289 3666948 3322485 3773747 3796479 3795436 2682562 3691755 

Figure 7: US Patents – Main island ’liquid-crystal display’ 



∗ 2-Mode Review – Given starting values of k1 and k2 the following 

list is computed: 

k1 k2 Rows Cols Comp 

where k1 is minimum degree in the first, k2 minimum degree in 

the second subset, Rows and Cols are number of vertices in first 

and second subset respectivelly and Comp, number of connected 

components in network induced by k1 and k2. k1 and k2 are incremented 

until the resulting network is empty. 

∗ 2-Mode Border – Compute only border values of k1 and k2 for 

a given 2-mode network. 

– Valued Core – Generalized k-core: Instead of counting lines (neighbors) 

use values of lines. sum of lines or maximum value can be used 

when computing valued core: 

Sum valued core of threshold val is a subnetwork of given network 

where the sum of values of lines to (from) the members of the same 

core is at least val. 

Max valued core of threshold val is a subnetwork of given network 

where the maximum value of all lines to (from) the members of the 

same core is at least val. 

Threshold values must be given in advance. Two different ways to 

determine thresholds: 

∗ First Threshold and Step – Select first threshold value and step 

in which to increase threshold. 

∗ Selected Thresholds – Thresholds (increasing numbers) are given 

using vector. 

∗ 2-Mode – valued core (according to line values) partition of a 2mode 

network. Given minimum valued degree in first (k1) and 

minimum valued degree in second subset (k2) a new partition is 

generated where 0 means that vertex does not belong to the valued 

core of prespecified k1 and k2, 1 means that vertex belongs to that 

core. 

Additionally (for 1-mode networks), Input, Output or All valued cores 

can be used. 

– Depth 

∗ Acyclic – Partition acyclic network according to depths of vertices. 

∗ Genealogical – Partition network that represents genealogy according 

to layers of vertices. 



∗ Generational – Partition network that represents genealogy according 

to layers of vertices. The same as genealogical partition 

but with less layers. 

– p-Cliques Partition network according to p-Cliques (partition to clusters 

where vertices have at least proportion p (number between 0 and 

1) neighbors inside the cluster. 

∗ Strong ... for directed network. 

∗ Weak ... for undirected network. 

– Vertex Labels – Partition vertices with same labels to the same class 

numbers (for molecule). 

– Vertex Shapes – Partition vertices with same shapes (ellipse, box, diamond) 

to the same class numbers (used in genealogy to show gender). 

– Islands – Partition vertices of network with values on lines (weights) 

to cohesive clusters (weights inside clusters must be larger than weights 

to neighborhood): the height of vertex (vector) is defined as the maximum 

weight of the neighbor lines. Two options: 

∗ Line Weights 

∗ Line Weights [Simple] 

New network with only lines constituting islands can be generated if 

Generate Network with Islands is checked. 

– Bow-Tie – Partition vertices of directed network (graph structure of 

the web) to the following classes: 1 – LSCC, 2 – IN, 3 – OUT, 4 – 

TUBES, 5 – TENDRILS, 0 – OTHERS. 

– 2-Mode – Partition of vertices of a 2-mode network into two subsets. 

– Default Labels Partition – Input is network with default vertex labels: 

e.g., v3, v9,... Result is a partition of selected dimension, where 

vertices defined by numbers stored in vertex labels (e.g., 3, 9,...) go to 

cluster 1, other vertices go to cluster 0. 

Operation can be used to make other objects (e.g. partitions, vectors, 

...) compatible with a network, if network is reduced by several operations 

(e.g. extractions). 

• Components 

– Strong – Strong Components of selected network. 

– Strong-Periodic – Strong Periodic Components of selected network - 

strongly connected components are further divided according to periods. 



Figure 8: Bow-tie – Graph structure in the web [26] 

– Weak – Weak Components of selected network. 

– Bi-Components – Biconnected Components of selected network. Articulation 

points belong to several classes, so the result cannot be 

stored in partition – biconnected components are stored in hierarchy! 

Minimal number of vertices in components can be selected. Additionally, 

partition containing articulation points is produced: number of 

biconnected components to which each vertex belongs is given. Partition 

containing vertices belonging to exactly one bicomponent, vertices 

outside bicomponents and articulation points is also produced: 

vertices outside bicomponents get class zero, each bicomponent is 

numbered consecutively (from 1 to number of bicomponents) and articulation 

points get class number 9999998. 

• Hierarchical Decomposition 

– Clustering* – Hierarchical clustering procedure. Input is dissimilarity 

network (matrix), which can be obtained using 

Operations/Dissimilarity/Network based or read from input file. 

∗ Run – Hierarchical clustering procedure. Result is hierarchy with 

nested clusters and dendrogram in EPS. 



∗ Options – Select method for hierarchical clustering procedure 

(general, minimum, maximum, average, ward, squared ward). 

– Symmetric-Acyclic – Symmetric-Acyclic decomposition of network. 

Result is hierarchy with nested clusters [33]. 

– Clustering with Relational Constraint – Hierarchical clustering with 

relational constraint procedure. See: 

Ferligoj A., Batagelj V. (1983): Some types of clustering with relational 

constraints. Psychometrika, 48(4), 541-552. 

Only dissimilarities among vertices that are linked are taken into account 

what enables to find clusterings very fast also for large networks. 

Input is network with dissimilarities, which can be obtained using 

Operations/Dissimilarity/Network or Vector based or read from input 

file. 

• Numbering 

∗ Run – Results are: a partition representing tree: fathers of nodes; 

and two vectors: describing heights of nodes and number of vertices 

in subtree respectivelly. If network has n vertices then obtained 

partitions and vectors have dimension 2*n-1. Note that 

this objects are not compatible with original network, you must 

use Make Partition to get compatible results. 

∗ Make Partition – From obtained partition representing tree generate 

partition compatible with original network 

· using Threshold determined by Vector – From obtained 

partition representing tree and one of the two vectors (all have 

dimension 2*n-1) generate partition compatible with original 

network by giving threshold value. 

· with selected Size of Clusters – From obtained partition representing 

tree and given number of vertices in clusters generate 

partition compatible with original network. 

∗ Extract Subtree as Hierarchy – Extract subtree from obtained 

Partition by giving the root as Pajek Hierarchy. 

∗ Options – Select method for hierarchical clustering with relational 

constraint (minimum, maximum, or average) and strategy 

(strict, leader, or tolerant). 

– Depth First – Depth first numbering of selected network... 

∗ Strong ... taking directions of arcs into account. 

∗ Weak ... forget directions (or undirected network). 



– Breadth First – Breadth first numbering of selected network... 

∗ Strong ... taking directions of arcs into account. 

∗ Weak ... forget directions (or undirected network). 

– Reverse Cuthill-McKee – RCM numbering. See paper. 

– Core + Degree – Numbering in decreasing order according to all core 

partition. Within the same core number vertices are ordered in decreasing 

order according to number of neighbors which have the same 

or higher core number. 

• Citation Weights – If a network represents citation network, weights of 

lines (citations) and vertices (articles) can be computed. Results are: 

– Network with values on lines representing importance of citations. 

– Binary partition with vertices on the main path. 

– Network containing only main path. 

– Vector with importance of vertices (articles). 

Different methods of assigning weights [43]: 

– Search Path Count (SPC) – method. Compute from Source to Sink. 

– Search Path Link Count (SPLC) – method. Each vertex is considered 

as Source. 

– Search Path Node Pair (SPNP) – method. 

Weights can also be normalized (using flow or maximum value) or logged. 

• k-neighbors – Select all vertices 

– Input ...from which we can reach selected vertex in at most k-steps. 

– Output ...that can be reached from selected vertex in at most k-steps. 

– All ...Input + Output (forget direction of lines) 

Result is partition where vertices are in class numbers equal to the distance 

from given vertex, vertices that cannot be reached from selected 

vertex are in class number 9999998. After you have a partition you 

can extract subnetwork. 

– From Clusters – Compute selected distances according to each vertex 

in Cluster. Results consist of so many partitions as is the number of 

vertices in cluster. Instead of storing results in partitions they can be 

stored in vectors as well. 



• Paths between 2 vertices 

– One Shortest – Find the shortest path between two vertices. Result 

is new network. Values on lines can be taken into account (if they 

present distances between vertices) or not (graph theoretical distance). 

The latter possibility is faster. 

– All Shortest – Find all shortest paths between two vertices. Result 

is new network. Values on lines can be taken into account (if they 

present distances between vertices) or not (graph theoretical distance). 

The latter possibility is faster. 

– Walks with Limited Length – Find all walks between two vertices 

with limited maximum length. 

– Diameter – Find diameter – the length of the longest shortest path in 

network and corresponding two vertices. Full search is performed, so 

the operation may be slow for very large networks (number of vertices 

larger than 2000). 

– Geodesics Matrices* – Compute the shortest path length matrix and 

the geodesics count matrix (for small networks only!). 

– Distribution of Distances – Compute distribution of lengths of the 

shortest paths and average path length among all reachable pairs of 

vertices in network. 

∗ From All Vertices – Take all vertices as starting points. 

∗ From Vertices in Cluster – Only distances from vertices selected 

by Cluster are computed. 

• Critical Path Method (CPM) – Find the critical path in acyclic network – 

result is new network containing the critical path. Algorithm can be used 

in the area of project planning but also for analysing acyclic graphs. Additional 

networks containing total and free delay times of activities are generated. 

Two vectors (partitions) are generated, too: First containing the earliest 

possible times of coming into given states and the second containing the 

latest feasible times of coming into given states. 

• Maximum Flow among vertices. 

– Selected Pair – Find maximum flow between selected two vertices 

(algorithm looks for paths to be saturated and among them it always 

selects the shortest path). Algorithm can be used in the technical area 

(actual flow, values on lines mean capacities) or for analysing graphs 

(if all values are 1). Result is a new network, containing the two vertices 

and lines contributing to maximum flow between them. 



– Pairs in Cluster – Find maximum flow among vertices determined by 

cluster. Result is a new network, where a value on line means maximum 

flow between corresponding two vertices. Algorithm is slow: 

Use it on smaller networks or clusters with limited number of vertices 

only! 

• Vector – Get vector from network 

– Centrality – Result is a vector containing selected centrality measure 

of each vertex and centralisation index of the whole network [64, p. 

169-219]. 

∗ Closeness centrality (Sabidussi). 

1. Input – centrality of each vertex according to distances of 

other vertices to selected vertex. 

2. Output – centrality of each vertex according to distances of 

selected vertex to all other vertices. 

3. All – forget direction of lines – consider network as undirected. 

∗ Betweenness centrality (Freeman). 

– Get Loops – store values of loops to vector. 

– Get Coordinate – x, y, or z coordinate of network. You can also get 

all coordinates at once - possibility to have more than 3 coordinates, 

coordinates must contain character . (dot). 

– Important Vertices – Find important vertices in directed network 

(e.g. web pages, scientific citations) or 2-mode network. Result are 

vectors with weights and partition with selected number of important 

vertices. 

∗ 1-Mode: Hubs-Authorities – In directed networks we can usually 

identify two types of important vertices: hubs and authorities 

[47]. A vertex is a good hub, if it points to many good authorities, 

and it is a good authority, if it is pointed to by many good hubs. In 

obtained partition value 1 means, that the vertex is a good authority, 

value 2 means, that the vertex is a good authority and a good 

hub, and value 3 means, that the vertex is a good hub. 

∗ 2-Mode: Important Vertices – Generalization of algorithm for 

2-mode networks – find important vertices from first and second 

subset. 

– Structural Holes – Burt’s measure of constraint (structural holes) [27, 

page 54-55]. Results are: 



∗ network pij: the proportion of the value of i’s relation(s) with j 

compared to the total value of all relations of i. where aij is the 

value of the line from i to j 

pij = 

aij + aji 

� 

k (aik + aki) 

∗ network containing dyadic constraint cij – the constraint of absent 

primary holes around j on i: Explanation: Contact j constrains 

your i’s entrepreneurial opportunities to the extent that: 

(a) you’ve made a large investment of time and energy to reach j, 

and 

(b) j is surrounded by few structural holes with which you could 

negotiate to get a favorable return on the investment. 

cij = (pij + � 

k,k�=i,k�=j 

pikpkj) 2 

∗ vector containing aggregate constraint Ci: Ci = � 

j cij, 

Ci = 1 for isolated vertices. 

– Clustering Coefficients – Compute different inherent tendency coefficients 

in undirected network: 

Let deg(v) denotes degree of vertex v, |E(G1(v))| number of lines 

among vertices in 1-neighborhood of vertex v, MaxDeg maximum 

degree of vertex in a network, and |E(G2(v))|, number of lines among 

vertices in 1 and 2-neighborhood of vertex v. 

∗ CC1 – coefficients considering only 1-neighborhood: 

CC1(v) = 

2|E(G1(v))| 

deg(v) · (deg(v) − 1) CC′ 1(v) = deg(v) 

MaxDeg CC1(v) 

∗ CC2 – coefficients considering 2-neighborhood 

CC2(v) = |E(G1(v))| 

|E(G2(v))| 

CC ′ 2(v) = deg(v) 

MaxDeg CC2(v) 

If deg(v) ≤ 1 all coefficients for vertex v get missing value (9999998). 

Watts-Strogatz Clustering Coefficient (Transitivity) and Network Clustering 

Coefficient are also reported. 

– Summing up Values of Lines – Sum values of all incoming, outgoing 

or all lines connected to selected vertex. 



– Min of Values of Lines – Find minimum value of incoming, outgoing 


– Max of Values of Lines – Find maximum value of incoming, outgoing 


– Centers – Find centers in a graph using ’robbery’ algorithm: vertices 

that have higher degrees (are stronger) than their neighbors steal from 

them: 

∗ at the beginning give to vertices initial strength according to their 

degrees, or start with value 1 

∗ when ’weak’ vertex is found, neighbors steal from it according to 

their strengths, or they steal the same amount 

– PCore – generalized cores. 

∗ Degree – ordinary cores. 

∗ Sum – taking values of lines into account (sum of values of lines 

inside pcore). 

∗ Max – taking values of lines into account (max of values of lines 

inside pcore). 

• Count - how many times each line belongs to predefined rings 

3.3 Nets 

– 3-Rings – For each line count number of 3-rings to which the line 

belongs. 

∗ Undirected – for undirected networks – count undirected 3-rings. 

∗ Directed – for directed networks – count cyclic, transitive, or all 

3-rings, or count how many times each line is a transitive shortcut 

(see Figure 9). 

– 4-Rings – For each line count number of 4-rings to which the line 

belongs. 

∗ Undirected – for undirected networks – count undirected 4-rings. 

∗ Directed – for directed networks – count cyclic, diamonds, genealogical, 

transitive, or all 4-rings, or count how many times each 

line is a transitive shortcut (see Figure 10). 

Operations on two networks. 



cyclic transitive 

Figure 9: Lines belonging to cyclic and transitive (shortcut) 3-rings 

cyclic transitive genealogical diamond 

Figure 10: Types of directed 4-rings on arcs 

• Union of lines – Fuse selected networks. Result is a multiple relations 

network. If you want to get union of networks, multiple lines must still 

be deleted. Networks must match in dimension or: If one network has m 

vertices and other n vertices and m < n then in network with n vertices first 

m vertices must match with vertices in network with m vertices. 

• Cross-Intersection – Intersection of selected networks. Networks must 

match in dimension or: If one network has m vertices and other n vertices 

and m < n then in network with n vertices first m vertices must match 

with vertices in network with m vertices. Values of lines in intercept can be 

sum, difference, product, quotient, min, or max of both values. 

• Intersection – Intersection of selected networks where relation numbers are 

taken into account. 

• Cross-Difference – Difference of selected networks. 

• Difference – Difference of selected networks where relation numbers are 

taken into account. 

• Union of vertices – Add the second network at the end of first network. 



• Fragment (1 in 2) – Find all instances of fragment (determined by network 

1) in network 2. 

– Find – Execute command. 

– Options Select appropriate model of fragment. 

∗ Induced – there should be no additional lines between vertices 

in instance of fragment to match (stronger condition) otherwise 

additional lines can be present (weaker). 

∗ Labeled – labels must match (e.g. atoms in molecule). Labels are 

determined by classes (colors) in partition - first partition and second 

partition must be selected before searching for labeled fragments. 

First partition determines ’labels’ of first network (fragment), 

second partition determines ’labels’ of second (original) 

network. 

∗ Check values of lines – values of lines must match (e.g. in genealogy 

values represent sex: 1 – man, 2 – woman). 

∗ Check relation number – relation numbers must match. 

∗ Check only cluster – only fragments are searched. where first 

vertex is one of the vertices in cluster. 

∗ Extract subnetwork – produce additional result: extract subnetwork 

containing vertices belonging to fragments and corresponding 

lines. 

· Retain all vertices after extracting – in extracted network 

the same vertices as in original network are present, only lines 

which do not belong to any fragment are removed. 

∗ Same vertices determine one fragment at most – how fragments 

on the same set of vertices are treated: if not checked – 

fragments with the same set of vertices are allowed. 

· Create Hierarchy with fragments – result of fragment searching 

is also a Hierarchy with vertices in fragments (available 

only if Same vertices determine one fragment at most is 

not checked. 

∗ Repeating vertices in fragment allowed – same vertices can appear 

in fragment more than once (e.g. in cycles). 

if not checked: found fragments always have the same number of 

vertices as original fragment 

if checked: some of found fragments can have less vertices than 

original fragment 



Michael/Zrieva/ 

Francischa/Georgio/ 

Damianus/Georgio/ 

Legnussa/Babalio/ 

Nicolinus/Gondola/ 

Franussa/Bona/ 

Marin/Gondola/ 

Magdalena/Grede/ 

Junius/Georgio/ 

Anucla/Zrieva/ 

Nicola/Ragnina/ 

Nicoleta/Zrieva/ 

Junius/Zrieva/ 

Margarita/Bona/ 

Sarachin/Bona/ 

Nicoletta/Gondola/ 

Marinus/Bona/ 

Phylippa/Mence/ 

Marinus/Zrieva/ 

Maria/Ragnina/ 

Figure 11: Fragments – Marriages among relatives in Ragusa 

Lorenzo/Ragnina/ 

Slavussa/Mence/ 

• Multiply First * Second - multiply selected 1 or 2 mode networks (that 

match criteria for multiplication). 

• Shrink coordinates (1 to 2) - Useful if you shrink network, draw shrunk 

network separately, and then apply all coordinates to vertices in original 

network (vertices in same class get the same coordinates). Replace coordinates 

in network 2 using coordinates of shrunk network 1. Shrinking can be 

determined using 

– Partition or 

– Hierarchy 

3.4 Operations 

One network and something else is needed as input. 

• Shrink Network - Before starting shrinking, select appropriate blockmodel 

in Options menu. Default is just number of lines between shrunk vertices 

that must be present in original network, to cause a line in a new network. 

– Partition – Shrink network according to selected partition. Vertices in 

class 0 are (by default) left unchanged, others are shrunk. Results are 

shrunken network and shrunken partition. 



– Hierarchy – Shrink network according to selected hierarchy. Nodes 

in hierarchy that are Closed are shrunk to new vertex. Cut nodes are 

shrunk to virtual vertex. Border nodes are not shrunk, but they are not 

visible. Vertices belonging to other nodes are left unchanged. Type of 

shrinking (blockmodel) can be selected in Options menu. 

• Extract from Network 

– Partition – Extract sub-network according to selected partition (extract 

range of classes from partition). Extracted partition is produced 

as additional result. 

– Cluster – Extract sub-network according to selected cluster. 

– 2-Mode Network – Extract 2-mode network from 1-mode network: 

first and second mode are determined by given set of clusters in partition. 

– to GEDCOM – Extract sub-genealogy according to selected partition 

(weakly connected component) to new GEDCOM file (genealogy 

must be read as Ore graph). 

• Brokerage Roles - For each vertex j count five brokerage roles (coordinator, 

itinerant broker, representative, gatekeeper and liaison) according to 

given partition. 

j 

i k 

coordinator 

• Dissimilarity* 

j 

i k 

itinerant broker 

j 

i k 

representative 

j 

i k 

gatekeeper 

j 

i k 

liaison 

– Network based – Compute selected dissimilarity matrix (d1, d2, d3 or 

d4) among vertices in cluster according to number of common neighbors. 

Corrected Euclidean-like d5 and Manhattan-like d6 dissimilarities 

can be computed as well [13]. The obtained matrix can be used 

further for hierarchical clustering procedure. 

You can include vertex v to its own neighborhood or not and display 

in report window only upper triangle / undirected or complete matrix 

/directed (if number of vertices is low). 



Nv is a set of input, output or all neighbors of vertex v; + stands for 

symmetric sum, ∪ stands for set union and \ stands for set difference; 

| stands for set cardinality; 1st maxdegree and 2nd maxdegree are the 

largest degree and the second largest degree in network, respectively. 

d1(u, v) = 

|Nu + Nv| 

1st maxdegree + 2nd maxdegree 

d2(u, v) = |Nu + Nv| 

|Nu ∪ Nv| 

d3(u, v) = |Nu + Nv| 

|Nu| + |Nv| 

d4(u, v) = max(|Nu 

d5(u, v) = 

\ Nv|, |Nv \ Nu|) 

max(|Nu|, |Nv|) 

� 

� 

� n� 

� 

� 

d6(u, v) = 

s=1 

s�=u,v 

((qus − qvs) 2 + (qsu − qsv) 2 ) + p · ((quu − qvv) 2 + (quv − qvu) 2 ) 

n� 

(|qus − qvs| + |qsu − qsv|) + p · (|quu − qvv| + |quv − qvu|) 

s=1 

s�=u,v 

Dissimilarities d5 and d6 are based on some matrix Q = [quv] on vertices 

– for example on adjacency matrix or on distance matrix. The 

parameter p is usually set to value 1 or 2. In the case Nu = Nv = 0 

we set all dissimilarities d1 - d4 to 1. 

If Among all linked Vertices only is checked dissimilarities are computed 

as line values of given network. 

– Vector based – Euclidean, Manhattan, Canberra, or (1-Cosine)/2 

dissimilarities among Vectors determined by Cluster are computed as 

line values of given network. 

• Vector – Operations on network and vector. 

– Network * Vector – Ordinary multiplication of matrix (network) by 

vector. Result is a new vector. 

– Vector # Network – Result is a new network: 

∗ Input – Multiplying incoming arcs in network by corresponding 

vector values - multiplying i-th column of matrix by i-th component 

of vector. 



∗ Output – Multiplying outgoing arcs in network by corresponding 

vector values - multiplying i-th row of matrix by i-th component 

of vector. 

– Harmonic Function – See Bollobas [25, page 328]. 

Let (G, a) be a connected weighted graph, with weight function a(x, y), 

and let S is subset of vertices V (G). A function f : V (G) → IR is 

said to be harmonic on (G, a), with boundary S, if 

f(x) = 1 

A(x) 

Implementation in Pajek: 

� 

(a(x, y)f(y)), ∀x ∈ V (G) \ S 

y 

A(x) = � 

a(x, y) 

y 

∗ function f is determined by vector 

∗ weight function a(x, y) is given by (valued) network 

∗ subset S is determined by partition – vertices in class 1 are in 

subset S (fixed vertices), other vertices are in V (G) \ S 

∗ additionally, permutation determines the order of vertices in computations. 

In Pajek you can compute the harmonic function once or iterativelly 

- as long as difference between successive functions become small 

enough. Components of vector that represents function f can be modified 

immediately when they are computed or only at the end of each 

iteration (after all components are computed). Procedure can be run 

according to: 

∗ Input – neighbors 

∗ Output – neighbors 

∗ All – neighbors 

– Summing up neighbors – For each vertex compute the sum of class 

numbers of its neighbors according to 




– Min of neighbors – For each vertex compute the minimum class number 

of its neighbors according to 






– Max of neighbors – For each vertex compute the maximum class 

number of its neighbors according to 




– Put Loops – put vector values as loops (arcs or edges) in current network. 

– Put Coordinate – put vector as x, y, or z coordinate, or put it as polar 

radius or polar angle of vertices in network layout. 

– Diffusion Partition – Compute diffusion partition according to thresholds 

given in vector. Vertices in selected cluster are considered to 

adopt in time 1. 

– Islands – Partition vertices to cohesive clusters according to weights 

of vertices determined by a vector. 

∗ Vertex Weights – Vertex island is a cluster of vertices of given 

network with weighted vertices where the weights of the vertices 

on the island are larger than the weights of the vertices in the 

neighborhood. The weights are also called heights. 

∗ Vertex Weights [Simple] – Simple vertex island is vertex island 

with only one top. 

• Transform – Transformations of network according to Partition, Cluster 

and/or Vector. 

– Remove Lines – Removing lines according to partition. 

∗ Inside Clusters – Remove all lines with incident vertices in the 

same (selected) cluster(s). 

∗ Between Clusters – Remove all lines with incident vertices in 

different clusters. 

∗ Between Two Clusters 

1. Arcs – Remove all arcs pointing from first to second cluster. 

2. Edges – Remove all edges between the selected two clusters. 

∗ Inside Clusters with value 

1. lower than Vector value – Remove all lines inside clusters 

(determined by a Partition) with value lower than the value 

specified in a Vector. 



2. higher than Vector value – Remove all lines inside clusters 

(determined by a Partition) with value higher than the value 

specified in a Vector. 

Dimension of a Vector must be equal to the highest cluster number 

in a Partition. 

– Add – some elements to network 

∗ Arcs from Vertex to Cluster – add arcs from selected vertex to 

all vertices in Cluster. 

∗ Arcs from Cluster to Vertex – add arcs from all vertices in Cluster 

to selected vertex. 

∗ Time Intervals determined by Partitions – change network to 

temporal network using two partitions: first partition determines 

initial time point, second determines terminal time point of each 

vertex. 

– Direction – Convert to directed network where all arcs are pointing 

from 

∗ Lower->Higher class number. 

∗ Higher->Lower class number. 

Lines inside classes may be deleted or not. 

– Vector(s) -> Line Values – Replace line values with result of selected 

operation (sum, difference, multiplication, division) on vector(s) values 

in corresponding terminal and initial vertices. 

• Reorder 

– Network – Reorder vertices in network according to selected permutation. 

– Partition – Reorder vertices in partition according to selected permutation. 

– Vector – Reorder vertices in vector according to selected permutation. 

• Count neighbor Colors – For selected network and partition a new partition 

is generated where for each vertex the frequency of vertices of selected 

color in the neighborhood is given. Colors to be counted are determined 

using cluster. 

• Coloring 

– Create New – Sequential coloring of vertices in order determined by 

permutation. Result depends on selected permutation significantly. 



– Complete Old – Complete partial coloring of vertices in order determined 

by permutation. For example some vertices can be colored by 

hand, but most of the vertices are still uncolored (in class 0). In this 

way you can help program to produce better coloring. 

• Balance* – Relocation algorithm for partitioning signed graphs (graphs 

with positive and negative values on lines representing friends and enemies, 

for example). Given partition is optimized to get as much as possible positive 

lines inside classes and negative lines between classes. Another algorithm 

does not distinguish between diagonal and off-diagonal blocks: each 

block can be positive, negative, or null. If number of repetitions is higher 

than 1, initial partitions into given number of classes are chosen randomly 

for every repetition separately. If program finds several optimal solutions, 

all are reported. For more details about algorithm see Doreian and Mrvar 

[32]. 

Option can be used for two mode signed graphs as well: input is two mode 

partition. In this case algorithm tries to find as ’clear’ as possible positive, 

negative, and null blocks. 

If Prespecification is checked user can define a prespecified model by entering 

letters P, N, or 0 to cells (to require positive, negative or null blocks) 

or leave cells empty (in this case the block can be of any type). 

By setting penalty for small null blocks to some nonzero value, we try to 

get null blocks as large as possible. 

• Blockmodeling* – Generalized blockmodeling of 1-mode and 2-mode networks 

[7, 35]. For details see Section 7 on page 84. Descriptions of models 

are stored on MDL files. See also block types on page 50. 

– Random Start – Start the optimization with random partition(s). 

– Optimize Partition – Show the criterion function for selected partition 

and optimize it. 

– Restricted Options – Show only selected part of options (sufficient 

for most users) or all options. 

– Short Report – Show only main results of optimization in Report 

window (sufficient for most users) or detailed, long report. 

• Genetic Structure – Compute genetic structure of given acyclic network 

according to given partition (of minimal vertices). As result we get as many 

vectors as is different clusters in partition, and the dominant gene partition. 

• Permutation* – Improve given permutation according to network. 



Pajek - shadow 0.00,1.00 Sep- 5-1998 

World trade - alphabetic order 

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Pajek - shadow 0.00,1.00 Sep- 5-1998 

World Trade (Snyder and Kick, 1979) - cores 

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Figure 12: World trade. Orderings: alphabetical and determined by clustering 

– Travelling Salesman – Can be applied to dissimilarity matrix, or modified 

matrix representing network (fill diagonal and change 0 in the 

matrix with some large numbers): 

∗ Run – Run 3-OPT algorithm for solving Travelling Salesman 

Problem. 

∗ Options – Put selected value on diagonal, add some artificial vertices, 

and incident lines with large values, change value 0 with 

selected (large) value. 

– Seriaton – Starting with network and (random) permutation improve 

the permutation using seriation algorithm from Murtagh [53, page 11- 

16]. 

∗ 1-Mode – for ordinary (1-Mode) networks 

∗ 2-Mode – for 2-Mode networks 

– Clumping – Starting with network and (random) permutation improve 

the permutation using clumping algorithm from Murtagh [53, page 11- 

16]. 

∗ 1-Mode – for ordinary (1-Mode) networks 

∗ 2-Mode – for 2-Mode networks 

– R-Enumeration – Starting with network and (random) permutation 

find such permutation that enumeration of neighbor vertices are as 

close to each other as possible. 



• Functional Composition – Let f be a partition or a permutation and g a 

partition, a permutation, or a vector. The result is new partition, permutation 

or vector r defined in the following way: r[v] = (f ∗ g)[v] = g[f[v]]. 

• Expand Partition 

– Greedy Partition – Put vertices with unknown class number (0) in the 

same class as selected vertices in partition if 

∗ Input ...we can reach selected vertices in at most k-steps. 

∗ Output ...we can come to vertices from selected vertices in at 

most k-steps. 

∗ All ...Input + Output (forget direction of lines) 

Classes are joined if one vertex should belong to more classes. 

– Influence Partition – Put every vertex with unknown class number (0) 

in given partition in the same class as is the class of the closest vertex. 

If several vertices with known class number have the same distance, 

the highest value is used. 

– Make Multiple Relations Network – Transform network to a multiple 

relation network using a partition: if both endvertices of a line 

belong to the same class in partition the multiple relations tag will be 

equal to the class number of endvertices, otherwise it will be 0. 

• Expand Reduction – Restore original network from reduced network (hierarchical 

reduction!) and appropriate hierarchy (result is always undirected 

network). 

• Identify – Identify (reorder and/or join some units). 

• Petri – Execute Petri net according to starting marking of places determined 

by partition. Number of places in network is equal to dimension of partition. 

Places must be defined first (1..m) then transitions (m + 1..n). What to do 

if more than one transition can fire? Two possibilities: 

– Random – Transition is chosen randomly. 

– Complete – Complete tree of all possible transitions is built - result is 

hierarchy. You can choose the maximum depth of the tree, or execute 

Petri net as long as possible. 

Try for example petri2 from the book of Peterson [56, page 21] or petri52 

(see Figure 13) data. 



E3 

E4 

C3 . 

. M4 M5 

M1. 

. 

C4 

. 

M3 

. 

C2 

. 

M2 . 

E5 

. 

. 

E2 

C5 

C1 

Figure 13: Petri net 

V. Batagelj and A. Mrvar Pajek 2.05 / September 24, 2011 

E1


• Refine Partition Refine partition according to selected network (reachability). 

– Strong ... for directed network. 

– Weak ... for undirected network. 

• Leader Partition – find clusters of vertices of network inside layers. 

3.5 Partition 

Only Partition is needed as input. 

• Create Constant Partition – Create constant partition of selected dimension. 

Default dimension is the size of selected network (if there is one in 

memory). 

• Create Random Partition – Create random one or two mode partition. 

• Binarize – Make binary (0-1) partition from selected partition. 

• Fuse Clusters – Fuse selected cluster numbers to a new cluster. 

• Canonical Partition – Transform partition to its canonical (unique) form 

(vertex 1 is always in class 1, the next vertex with smallest number that is 

not in the same class as vertex 1 is in class 2...). 

• Canonical Partition [Decreasing frequencies] – Transform partition to its 

canonical (unique) form (in class 1 the old class with the highest frequency 

will be set, in class 2 the old class with the second highest frequency. . . ). 

• Make Network – Generate network from partition. 

– Random Network – Generate random network where degrees of vertices 

are determined using partition. 

∗ Undirected – partition gives degrees of vertices in undirected network. 

∗ Input – partition gives input degrees of vertices. 

∗ Output – partition gives output degrees of vertices. 

– 2-Mode Network – Generate 2-mode network: first set consists of 

vertices (v1 . . . vn), second set consists of clusters (c0 . . . cm). If vertex 

i is in cluster j the line from vi to cj is generated. If option Existing 

Clusters only is selected only clusters containing at least one vertex 

are generated as vertices in the second set. 



• Make Permutation – Make permutation from selected partition. (first all 

vertices with the lowest class number, ...) 

• Make Cluster – Transform partition to cluster. 

• Make Hierarchy – Transform partition to hierarchy (nested or not). 

• Make Vector – Transform partition to vector (V [i] := C[i]). 

• Count, Min-Max Vector – info about cluster frequencies and minimum 

and maximum vector value according to given partition. 

3.6 Partitions 

Operations on two partitions. Two partitions must be selected before performing 

operations. 

• Extract second from first – Extract from first partition vertices that satisfy 

criterion (are on specified interval) determined by second partition. This 

operation is useful when we have partition that actually saves some information 

about vertices (for example gender). When you get (extract) some 

smaller part of the network (for example vertices that are on distances less 

than 3 from selected vertex), information about gender would be lost without 

performing the same operation (extraction) on partition. 

• Add Partitions – Add two partitions (useful for example when combining 

Input and Output neighbors in acyclic networks). 

• Min (C1, C2) – Minimum of two partitions. 

• Max (C1, C2) – Maximum of two partitions. 

• Fuse Partitions – Fuse two partitions – add second to the end of the first 

(useful for 2-mode networks). 

• Expand – Expand partition to higher (original) dimension. 

– First according to Second (Shrink) – Expand first partition according 

to shrinking determined by second partition. 

– Insert First into Second according to Third (Extract) – The current 

partition was obtained by extracting selected classes defined by the 

second partition from the first partition. This sub-partition was modified. 

Using this operation we can insert this modified sub-partition 

back to the first partition. 



• Intersection – of selected partitions. 

• Cover with – Let p be a partition, b a binary partition, and c selected cluster 

number. Result is new partition q determined in the following way: 

if b(v) = 0 then q(v) = p(v) else q(v) = c. 

• Merge – Let p and q be partitions and b a binary partition. Result is new 

partition s determined in the following way: 

if b(v) = 0 then s(v) = p(v) else s(v) = q(v). 

• Make Random Network – generate random network with input degrees 

determined by the first and output degrees by the second partition. 

• Info – Bivariate statistical measures between selected partitions: 

3.7 Vector 

– Cramer’s V, Rajski, Adjusted Rand Index – Report contingency 

table, compute Cramer’s V, Rajski coefficients, and Adjusted Rand 

Index. 

– Spearman Rank correlation coefficient. 

Operations using vector. 

• Create Constant Vector – Create constant vector (vector with all values 

equal to selected value) of selected dimension. Default dimension is the 

size of selected network (if there is one in memory). 

• Extract Subvector – Extract subvector from given vector - criterion is class 

in the selected partition. 

• Shrink Vector – Shrink vector values according to clusters of partition to 

new vector – adjusting vector to shrunken network. When shrinking several 

values to one value, sum of values, mean, min, max or median value can be 

used. 

• Make Partition – Convert vector to partition: 

– by Intervals – according to selected dividing numbers in vector vertices 

get appropriate class numbers. Intervals can be given by: 

∗ First Threshold and Step – Select first threshold and step in 

which to increase threshold. 



∗ Selected Thresholds – Select all thresholds or number of classes 

(#) in advance. 

– by Truncating (Abs) – partition is absolute and truncated vector. 

• Make Permutation – Convert vector to permutation - sorting permutation. 

• Make 2-Mode Network – Convert vector to 2-mode network (row or col). 

• Transform – Transformations of given vector: 

– Multiply by a constant. 

– Add Constant to vector values. 

– Absolute values of its elements. 

– Absolute + Sqrt – square root of its absolute components. 

– Truncate – truncated vector. 

– Exp – exponential of vector. 

– Ln – natural logarithm of vector. 

– Power – selected power of vector. 

– Normalize 

3.8 Vectors 

∗ Sum – normalize so that the sum of elements is 1. 

∗ Max – normalize so that the maximum element will have value 1. 

∗ Standardize – normalize so that arithmetic mean will be 0 and 

standard deviation 1. 

– Invert – inverse values of vector (exception is that 0 stays 0). 

Operations on two vectors. Two vectors must be selected before performing operations. 

• Add Vectors – sum of selected vectors. 

• Subtract Second from First – difference of selected vectors. 

• Multiply Vectors – product of selected vectors. 

• Divide First by Second – division of selected vectors. 

• Linear Regression – fit the two vectors using linear regression. Results are: 

regression line, linear estimates of second vector and corresponding errors. 



• Min (V1, V2) – smaller elements in selected vectors. 

• Max (V1, V2) – bigger elements in selected vectors. 

• Fuse Vectors – fusion of vectors. 

• Transform – two vectors to another two vectors: 

– Cartesian → Polar – First vector must contain x-coordinates second 

y-coordinates. Results are: vector containing polar radius and vector 

containing polar angles in degrees. 

– Polar → Cartesian – First vector must contain polar radius second 

polar angles in degrees. Results are: vector containing x-coordinates 

and vector containing y-coordinates. 

Results can be (de)normalized to enable direct use in Draw window. 

• Info – Pearson correlation coefficient between selected vectors. 

3.9 Permutation 

Only permutation is needed as input. 

• Identity – Create identity permutation of selected dimension. Default dimension 

is the size of selected network (if there is one in memory). 

• Random – Create random permutation of selected dimension. Default dimension 

is the size of selected network (if there is one in memory). 

• Random 2-Mode – Create random permutation of selected dimension and 

number of vertices in the first subset of 2-mode network. Default dimension 

is the size of selected network and number of vertices in the first subset (if 

there is network and corresponding partition in memory). 

• Inverse – Create inverse permutation of selected permutation. 

• Mirror – Create mirroring permutation of selected permutation (sort in opposite 

direction). 

• Make Partition – Create partition into selected number of clusters from 

given permutation. 

• Make Vector – Transform permutation to vector. 



3.10 Permutations 

Operation on two permutations. 

• Fuse Permuations – Fuse two permutations – add second to the end of the 

first (useful for 2-mode networks). 

3.11 Cluster 

Only cluster (and partition) is needed as input. 

• Create Empty Cluster – Create cluster without vertices. 

• Create Complete Cluster – Create cluster with values 1..n. 

• Make Partition – Transform cluster to partition. 

• Binarize Partition – Binarize partition according to cluster - make binary 

partition of the same dimension as the given partition, vertices that are in 

cluster numbers determined by the cluster will go to class 1 other to class 0. 

This allows noncontiguous ranges to be selected (other choices in Pajek 

need contiguous ranges). Note the exception: In this case cluster represents 

set of cluster numbers and not set of vertices numbers. 

3.12 Hierarchy 

Only hierarchy is needed as input. 

• Extract Cluster – Extract cluster from hierarchy - the cluster is whole subtree 

of selected node in hierarchy. 

• Make Network – Converts hierarchy to network (use it for example to draw 

hierarchy – drawing by layers). Closed nodes are also taken into account. 

• Make Partition – Converts hierarchy to partition (according to closed nodes). 

• Make Permutation – Converts hierarchy to permutation. 

• Export as Dendrogram to EPS – Draw dendrogram of hierarchy in EPS. 

Works for binary hierarchies only. Dissimilarities must be stored in names 

of nodes of hierarchy between [ and ]. These are obtained automatically 

when obtaining hierarchies using hierarchical clustering or clustering with 

relational constraint. 



3.13 Options 

• Read - Write 

– Threshold – Value of line must be higher (absolutely) than the given 

threshold to generate line between two vertices. 

– Max. vertices to draw – Maximum number of vertices in network to 

allow drawing (to prevent long waiting). 

– Large Network (Vertices) – Select the threshold number of vertices 

that defines very large network. For such networks Pajek (for some 

operations), asks if the old network can be destroyed and replaced by 

the network that is obtained as a result. In this way we can spare a lot 

of memory. 

– Read - Save vertices labels? – Read / Save also labels, coordinates, 

and other descriptions of vertices or not. If vertices labels are not read 

(recommended if network is very large and vertices labels are long) 

they can be imported later from input file using 

Net/Transform/Add/Vertex Labels from File. 

– Save coordinates of vertices? – Save coordinates of vertices to network 

file (or not). 

– Save complete vertex description? – When saving network to output 

file for each vertex complete description will be written, even if 

consequent vertices have the same descriptions (e.g. shapes, time intervals...). 

– Check equality of vertex descriptions by reading? – Enables users 

to speed up reading large network files according to descriptions of 

vertices: Check this option to save space when exactly the same descriptions 

of vertices are repeated often (e.g. shapes of vertices). Uncheck 

this option to save time when there are several different desctriptions 

of vertices in input file (e.g. time stamps in temporal networks). 

– Check equality of line descriptions by reading? – Enables users to 

speed up reading large network files according to descriptions of lines: 

Check this option to save space when exactly the same descriptions of 

lines are repeated often (e.g. line pattern Dots/Solid). Uncheck this 

option to save time when there are several different desctriptions of 

lines in input file (e.g. time stamps in temporal networks). 

– Auto Report? – Automatically report all text results to file rep1.rep. 

– Ore: Different relations for male and female links – When reading 

genealogy as Ore graph generate 2 different types of arcs: arc with relation 

number 1 (also value 1) represents (god)father to child relation, 



arc with with relation number 2 (also value 2) represents (god)mother 

to child relation. 

– Ore: Generate Godparent relation – When reading genealogy as 

Ore graph generate also godparent relation (relation number 4) or godfather 

(relation number 4) and godmother (relation number 5) relations. 

– GEDCOM – Pgraph – Use pgraph format (nodes are couples or individuals) 

when reading genealogies (D. R. White), otherwise nodes are 

only individuals. 

– Bipartite Pgraph – Generate bipartite pgraph that has squares for 

marriages, triangles and circles for individuals. 

– Pgraph+labels – Attach also labels of lines to pgraph, when reading 

GEDCOM file. 

– x / 0 = Specify the result when dividing nonzero value with 0. 

– 0 / 0 = Specify the result when dividing 0 with 0. 

– Ignore Missing Values in Info/Vector? – When computing descriptive 

statistics on Vector treat missing values (values larger that 9999997) 

as valid numbers. 

– Save Files as Unicode UTF8 with BOM? – Instead of saving to 

ASCII files save files as Unicode UTF8 files. 

• Select Font 

– Select Proportional Font – Select proportional font for displaying 

Unicode characters (e.g. in Draw window). 

– Select Monospaced Font – Select non-proportional font for displaying 

Unicode characters (e.g. in Report window). 

– Default Fonts – Use MS Sans Serif for proportional, and Courier New 

for monospaced font. 

• Main Window Colors - Select color for panels, color for drop-down menus 

and color for font used in Pajek main window. 

• Blockmodel – Select type of blockmodel for shrinking. Possibilities are: 

– 0..Min Number of Links 

– 1..Null 

– 2..Complete 



Figure 14: Generalized block types 



– 3..Row-Dominant 

– 4..Col-Dominant 

– 5..Row-Regular 

– 6..Col-Regular 

– 7..Regular 

– 8..Row-Functional 

– 9..Col-Functional 

– 10..Degree Density 

Look in Batagelj [7] and Doreian, Batagelj, Ferligoj [35]. 

• Ini File 

– Load – Use selected configuration of Pajek which is stored in the 

file (*.ini). 

– Save – Save the current configuration of Pajek into a file (*.ini). 

• Use Old Style Dialogs – If Windows 7 have problems with opening/saving 

files check this option. 

3.14 Info 

• Network – Information about network 

– General – General information about network 

∗ number of vertices 

∗ number of arcs, edges and loops 

∗ density of lines 

∗ average degree 

∗ sort lines according to their values (ascending or descending) to 

find the most/least important lines. 

– Line Values – Frequency distribution of line values. 

– Indices – Different indices on network (chemical and genealogical). 

– Triadic Census – Number of different triads in network. See book of 

Faust and Wasserman [64] and Figure 15 on page 55. 

– Multiple Relations – General information about multiple relations 

network 



∗ number of relations 

∗ number of arcs, edges and total number of lines for each relation 

– Vertex Label -> Vertex Number – Find vertex number by giving 

(part of) its label, or find vertex label for given vertex number. 

• Partition – General information about partition. Sort vertices according 

to their class numbers (ascending or descending) to see the most important 

vertices. Frequency distribution of class numbers. Average, median and 

standard deviation of class numbers are also given. 

• Hierarchy – General information about hierarchy. Operation is possible 

only if node numbers are integers. It returns number of vertices in nodes of 

hierarchy (on first level). 

• Vector – General information about vector: Vertices sorted according to 

their values, average, median, standard deviation and frequency distribution 

of vector values into given number of classes (# – number of classes or 

selected dividing values can be given). 

• Memory – Available memory. Not very accurate. 

• About – Information about Pajek version, authors, copyrights. . . 

3.15 Tools 

• R 

• SPSS 

– Send to R – Call statistical package R [57] with one vector/network, 

vectors/networks selected by cluster or all currently available vectors 

and/or networks. 

– Locate R – locate position of statistical program R (Rgui.exe or Rterm.exe) 

on the disk. 

– Send to SPSS – Call statistical package SPSS with one partition, vector 

or network, partitions/vectors selected by cluster or all currently 

available partitions and vectors. 

– Locate SPSS – locate position of statistical program SPSS (runsyntx.exe) 

on the disk. 



• Export to Tab Delimited File – Export Networks, Partitions, and Vectors 

to tab delimited file. This file can then be imported to other programs, like 

statistical packages, Excel... 

• Web Browser – Select which web browser to open when clicking on vertex 

with Shift and Right mouse button. 

• Add Program – add new executable program with specified parameters to 

the tools menu. 

• Edit Parameters – edit parameters of selected external program. 

• Remove Program – remove selected external program from the tools menu. 



1 - 003 

5 - 021U 

9 - 030T 

13 - 120U 

2 - 012 

6 - 021C 

10 - 030C 

14 - 120C 

3 - 102 

7 - 111D 

11 - 201 

15 - 210 

Figure 15: All different triads. 

4 - 021D 

8 - 111U 

12 - 120D 

16 - 300 


56 Pajek– Draw window 

4 Draw Window Tools 

4.1 Main Window Draw Tool 

• Draw - Draw Network. A new window is open, where a new menu appears. 

You can edit network by hand (move vertices using left mouse button), select 

a part of the picture (using right mouse button and select the area), edit 

lines that belong to selected vertex by clicking on vertex using right mouse 

button, spin picture using keys X, Y, Z, S, x, y, z, s. Description of Draw 

window menu: 

• Draw-Partition – Similar to Draw. Colors of vertices represent the classes 

in selected partition. Additionally you can put selected vertex or selected 

vertices into given class in partition (classes are shown using different colors) 

by clicking on middle mouse button (or Shift+left button) (increment 

class), or together with Alt (or Alt+left button) - decrement class number. 

In Figure 20 on page 90 you can see which color represents selected class. 

Some additional menu items that were already described appeared (you can 

draw network according to layers from partition and optimise energy using 

fixed vertices determined using partition). It is also possible to move the 

selected class (by clicking close to vertex from that partition). 

• Draw-Vector – Sizes of vertices are determined using selected vector. 

• Draw-2Vectors – Sizes of vertices are determined using selected two vectors 

(first for width second for height). 

• Draw-Partition-Vector – Colors of vertices are determined using selected 

partition, sizes of vertices are determined using selected vector. 

• Draw-Partition-2Vectors – Colors of vertices are determined using selected 

partition, sizes of vertices are determined using selected two vectors 

(first for width second for height). 

• Draw-SelectAll – Create null partition and draw network using it. 

4.2 Layout 

Generate layout of the network. 

• Circular – Position vertices on circle 

1. Original – in order determined by the network. 


Pajek– Draw window 57 

2. using Permutation – in order determined by current permutation. 

3. using Partition – create separate circles for clusters in selected partition. 

Center of the circle is determined by the arithmetic mean of 

positions of vertices in the cluster. 

4. Random – in random order. 

• Energy – Automatic layout generation. 

1. Kamada-Kawai – algorithm for automatic layout generation in the 

plane. 

(a) Free – Every position in the plane is possible. 

(b) Separate Components – Optimize each component separatelly 

and tile components at the end. 

(c) Fix first and last – First and last vertex are fixed in opposite corners. 

(d) Fix one vertex in the middle - Select vertex which will be fixed 

in the middle of the picture. 

(e) Selected group only – Only selected part of the picture is taking 

into account during optimisation. 

(f) Fix selected vertices - Selected vertices (from partition) are fixed 

on given positions). This item is visible only if Draw partition is 

active. 

2. Fruchterman Reingold – another algorithm for automatic layout 

generation (faster than Kamada-Kawai). 

(a) 2D – optimisation in plane. 

(b) 3D – optimisation in space. 

(c) Factor – Input factor for optimal distance among vertices when 

using Fruchterman Reingold optimisation. 

3. Starting positions – for energy drawing (random, circular, given positions 

on plane xy, given z coordinates). 

• EigenValues – Drawing using eigenvalues/eigenvectors (Lanczos algorithm). 

Values of lines can be taken into account or not. 

1. 1 1 1 – Select 2 or 3 eigenvalues and algorithm will compute corresponding 

eigenvectors. Eigenvalues may be multiple so there are 

many possibilities. Some examples 

(a) 1 1 1 – compute 3 eigenvectors that correspond to the first eigenvalue 



Figure 16: VRML display of layout determined by eigenvectors 

(b) 1 1 2 – compute 2 eigenvectors that correspond to the first eigenvalue 

and 1 that correspond to the second 

(c) 1 2 2 – compute 1 eigenvector that correspond to the first eigenvalue 

and 2 that correspond to the second 

(d) 1 2 3 – compute 1 eigenvector that correspond to the first, 1 

that correspond to the second and 1 that correspond to the third 

eigenvalue 

(e) 1 1 – compute 2 eigenvectors that correspond to the first eigenvalue 

(2D picture) 

• Tile Components – Tile weakly connected components in a plane. 

4.3 Layers 

Visible only if Draw partition is active. Draw in layers according to partition. 

• Type of Layout – Select type of picture (2D – layers in y direction, or 3D 

– layers in z direction). According to that, appropriate menu appears. 

• In y direction – Draw vertices in layers (y coordinate) inside layers draw 

vertices centered-equidistantly (x coordinate), z coordinate is 0.5 for all vertices. 



• In y direction+random in x – Same as first option, only vertices are put on 

layers in random order not according to vertex numbers. 

• In z direction – Draw layers in z direction, live x and y coordinates as they 

are. 

• In z direction + random in xy – Draw layers in z direction, x and y coordinates 

get random values 

• Averaging x coordinate – Use it after vertices are put on layers in 2D. 

Iterativelly compute average x-coordinate of all neighbors and normalize. 

Good approximation of global picture, but vertices are put to close to each 

other. Use it on all vertices or only on selected one. 

• Averaging x and y coordinates – Use it after vertices are put on layers in 

3D. Iterativelly compute average x and y coordinates of all neighbors and 

normalize. Good approximation of global picture, but vertices are put to 

close to each other. Use it on all vertices or only on selected one. 

• Tile in x direction – After averaging x coordinate vertices are put to close to 

each other, so using this option vertices are repositioned to minimal distance 

described in resolution. 

• Tile in xy plane – Same as previous, only this option is used when drawing 

3D pictures. 

• Optimize layers in x direction – Optimize layout in layers using minimization 

of the total length of lines. 

1. Forward – go from first to last layer. In the current layer optimize 

only layers having numbers equal or one smaller as the current layer 

number. 

2. Backward – go from last to first layer. In the current layer optimize 

only layers having numbers equal or one larger as the current layer 

number. 

3. Complete – go from first to last layer. In the current layer optimize 

only layers having numbers equal or one smaller or one larger as the 

current layer number. 

• Optimize layers in xy plane – Same as previous, only this option is used 

when drawing 3D pictures. 



• Resolution – How many additional positions are available on layers. Works 

only if Pgraph is selected. The higher the resolution, the better is the result 

of optimization, but also slower. 

4.4 GraphOnly 

Show complete picture without labels and arrows. 

4.5 Previous 

Draw previous network, and/or partition and/or vector which are loaded in Pajek 

(depending on selection in Options/PreviousNext/Apply to). 

4.6 Redraw 

Redraw network. 

4.7 Next 

Draw next network, and/or partition and/or vector which are loaded in Pajek 

(depending on selection in Options/ PreviousNext/ Apply to). 

4.8 ZoomOut 

Zoom out (visible only when zooming in layout). 

4.9 Options 

Additional options for picture layout. 

• Transform – Transformations of picture. 

1. Fit area 

(a) max(x), max(y), max(z) – Draw picture as big as possible to fit 

area (resize each coordinate to fit in picture independently). 

(b) max(x,y,z) – Resize to fit in area but keep real proportions (resize 

according to largest distance in all three coordinates, e.g. 

molecule). 

2. Resize – Resize picture (or selected part of it) in all three directions 

for selected factor. 



3. Translate – Translate picture (or selected part of it) in space. 

4. Reflect y axis – Reflect picture (or selected part of it) around y axis. 

5. Rotate 2D – Rotate picture (or selected part of it) in xy plane. 

6. Fisheye – Fisheye transformation (cartesian or polar) of picture. If no 

vertex is selected the middle point of picture (or selected part of it) is 

used as focus, otherwise first selected vertex will be used as focus. 

• Values of lines – Meaning of values of lines during energy drawing or 

eigenvectors computing (no meaning, similarities, dissimilarities (distances)). 

• Mark vertices using – Labels can be marked using 

1. labels 

2. numbers 

3. partition clusters (if partition of the same size is also selected) 

4. vector values (if vector of the same size is also selected) 

5. without labels 

6. without labels and arrows 

7. cluster only – only vertices belonging to the current Cluster are labeled 

in the layout. 

• Lines – Select the way the lines are drawn: 

1. Draw Lines 

(a) Edges – draw edges or not 

(b) Arcs – draw arcs or not 

(c) Relations – draw all lines (leave empty string) or just lines belonging 

to selected relations, e.g. 1-3,6,10-15. 

2. Mark Lines 

(a) No – do not mark lines 

(b) with Labels 

(c) with Values 

3. Different Widths – if checked, the width of the lines will be determined 

by their line values. 

4. GreyScale – if checked, the color in grayscale of lines will be determined 

by their line values. 



• Size – Determine size of vertices, width of vertices border, width of lines, 

size of arrows, size of font or turn them to default values. 

Sizes of vertices can be set to autosize (0-average). They can be read from 

input file (x fact and y fact) or determined by one vector (currently selected) 

or the two currently selected vectors. FontSize can be proportional to values 

stored in third partition. 

• Colors – Determine color of background, vertices, border of vertices, edges, 

arcs and font (of vertices labels and lines labels) or turn them to default 

values. Colors of edges/arcs can represent relation number of lines. You 

can select which color should represent given class using Relation Colors. 

You can also use colors of vertices (ic Red), border of vertices (bc 

Blue), arcs and edges (c Green) as defined on input file (see Figure 19, 

page 89). FontColor can be determined by values stored in second partition. 

Additionally to predefined colors it is possible to specify colors using RGB 

(e.g. RGBFF0000, or RGB(1,0,0)) and CMYK (e.g. CMYK00FF0000, 

or CMYK(0,1,0,0)) format. Note that there should be no spaces in string 

defining a color. 

Example NET file: 

*Vertices 9 

1 "a" ic Pink bc Black 

2 "b" ic CMYK(0,0,1,0.0) bc CMYKFF000000 

3 "c" ic Cyan bc Yellow 

4 "d" ic Purple bc Orange 

5 "e" ic Orange bc Brown 

6 "f" ic Magenta bc Green 

7 "g" ic Brown bc Magenta 

8 "h" ic RGB(1,0,0) bc Blue 

9 "i" ic Green bc Magenta 

*Arcs 1 2 1 c RGB0000FF 

2 3 1 c Red 

3 4 1 c Black 

4 5 1 c Yellow 

5 6 1 c Gray 

6 7 1 c Cyan 

7 8 1 c Magenta 

8 9 1 c Purple 

9 1 1 c Brown 

• Layout – Layout options 

1. Redraw – Redraw whole network during or/and after moving of selected 

vertex, and/or redraw if draw window is paint. 

2. Real xy proportions – The draw window has always square shape or 

not. 



3. Arrows in the Middle – Draw arrows in the middle of lines – not at 

terminal vertices. 

4. Size of vertex 0 – How to handle vertices of size 0 (size of vertex is 

determined in input file or using vector)? 

(a) Hide vertex – vertices of size 0 are shown or not. 

(b) Hide attached lines – lines with one end in vertex of size 0 are 

shown or not. 

5. Decimal Places – How many decimal places to use when marking 

vertices using vectors. 

6. Show SubLabel – Select the position of the vertices sublabel that is 

shown in network layouts. 

• ScrollBar On/Off – Show/Hide the scrollbars in the top left corner of Draw 

window. When part of picture is selected, scrollbar is used for moving. 

When whole picture is selected, scrollbar is used for spinning (like pressing 

keys X, Y, Z, x, y, z – spinning around axis defined by the key, and S – spin 

around selected normal) 

• Interrupt – Interrupt period during optimisation (stop every ? second, or 

not) 

• Previous/Next – Select parameters when using Previous or Next commands 

for drawing sequence of networks in draw window: 

1. Max. number – How many networks to show in sequence. If the 

number is higher than number of existing networks the sequence will 

stop earlier. 

2. Seconds to wait – Seconds to wait between the two layouts. 

3. Optimize Layouts – Optimize the current layout or not. If the sequence 

of networks is obtained from the same network, it is useful to 

choose Energy/Starting Positions/ Given xy to start optimization with 

existing coordinates. 

(a) Kamada-Kawai – Optimize the current layout using 

Kamada-Kawai algorithm. 

(b) 2D Frucht. Rein. – Optimize the current layout using 2D Frucht. 

Rein. algorithm. 

(c) 3D Frucht. Rein. – Optimize the current layout using 3D Frucht. 

Rein. algorithm. 

(d) No – Do not optimize the layout, just show the picture. 



4. Apply to – Which object (Network, Partition, Vector) will change 

when Previous or Next is selected: 

(a) Network – The previous / next network in memory is drawn. If 

Draw-Partition is selected and the new network matches in dimension 

with selected partition, the same partition will determine 

colors of vertices of the new network. If Draw-Vector is selected 

and the new network matches in dimension with selected vector, 

the same vector will determine sizes of vertices of the new network. 

Option can be used to show several networks of equal size using 

the same partition/vector. 

(b) Partition – The previous / next partition in memory is selected. If 

Draw-Partition is selected: The same network is drawn using previous 

/ next partition (network and partition must match in size). 

Option can be used to show several partitions of selected network. 

(c) Vector – The previous / next vector in memory is selected. If 

Draw-Vector is selected: The same network is drawn using previous 

/ next vector (network and vector must match in size). 

Option can be used to show several vectors of selected network. 

By checking several objects (Network, Partition, Vector) at the same 

time previous / next networks will be drawn using previous / next partitions 

and (or) vectors at the same time. All consequent selected objects 

must match in size. 

• Select all – Select all vertices in window (then possible to put vertices in 

given class). 

4.10 Export 

Export layout of the network to one of the following two or three dimensional 

formats: 

• 2D – two dimensional exports: 

– EPS/PS – Export to EPS format (with or without Clip, or WYSIWYG 

[What You See Is What You Get – exported EPS picture is similar to 

picture in Draw window – except that colors are Black/White or color 

determined by partition]). PS – Export to PS format (similar to EPS 

but without header). 



– SVG – Export to SVG (Scalable Vector Graphics) format. Additional 

controls over layout can be included in SVG or HTML. The plugin for 

examining layouts can be obtained from Adobe [1]. 

Linear or radial gradients (continuously smooth color transitions from 

one color to another) can be selected as well – up to three background 

colors can be selected in Export/Options window. 

1. General – Export to SVG without possibility to choose parts of 

the picture. 

2. Labels/Arcs/Edges – Export with possibility to turn labels, arcs 

and/or edges on/off. 

3. Partition – Export to SVG using one or two partitions. One partition 

is used by default: the same partition determines classes and 

colors. But, if two partitions are defined by Partitions menu, first 

partition will determine classes, the second colors of vertices. 

(a) Classes – User can turn selected classes and lines among 

classes on/off. 

(b) Classes with semi-lines – User can turn selected classes on/off. 

Lines among classes are drawn as semi-lines. 

(c) Nested Classes – Upper classes are nested in lower – whenever 

selected class is turned on all higher classes are turned on 

too, and all lower classes are turned off (suitable for showing 

cores, for example). 

4. Line Values – Export to SVG using values of lines. Threshold 

values or number of classes must be given. If you input #n, n 

classes of equal size will be generated. According to obtained 

thresholds, subsets of lines (and incident vertices) are defined and 

can be turned on/off inside web browser. 

(a) Classes – User can turn lines of selected value and incident 

vertices on/off. 

(b) Nested classes – User can turn lines of selected value or 

higher (lower) and incident vertices on (off). 

(c) Options – Additional options to emphasize the values of lines 

using some visual properties. 

Different Colors – Subsets of lines are drawn using colors 

which are used for partitioning vertices too. 

Using GreyScale – The darkness of a line corresponds to its 

value. 

Different Widths – The width of a line corresponds to its 

value. 



5. Multiple Relations Network – Export multiple relations network 

to SVG. User can show/hide one or more relations in the layout. 

6. Current and all Subsequent – If checked the current network 

and all subsequent networks will be exported to SVG. For each 

network separate html file is generated. Files are given the following 

names: file001.htm, file002.htm,... Generated html files 

get additional links (Previous/Next) to transition among them. If 

also next partitions / vectors fit in dimension to dimension of networks, 

partitions will determine color of vertices, vectors will determine 

sizes of vertices. Subsequent is applied to any combination 

of [Network, Partition, Vector] (one of the three objects only, 

any pair of them or all three of them) according to selection in 

Options/Previous/Next/ Apply to in Draw window. 

– Bitmap – Export to Windows bitmap (bmp) format. 

• 3D – three dimensional exports: 

– X3D – Export to X3D (XML based 3D computer graphics, the successor 

of VRML) format. 

– Kinemages – Export to Kinemages format with balls or labels. You 

need Mage or King viewer to watch it. A free copy of the Mage software 

can be downloaded from its site [58]. 

1. Current Network Only – Export only current network to Kinemages. 

Two partitions defined by Partitions menu can be used - 

one for generations one for colors. 

2. Current and all Subsequent – Export current network and all 

subsequent networks (use commands KINEMAGE/Next or Ctrl 

N in Mage). If also next partitions/vectors fit in dimension to dimension 

of networks, partitions will determine color of vertices, 

vectors will determine sizes of vertices. Subsequent is applied to 

any combination of [Network, Partition, Vector] (one of the three 

objects only, any pair of them or all three of them) according to 

selection in Options/Previous/Next/ Apply to in Draw window. 

3. Multiple Relations Network – Export with possibility to hide / 

show selected relations. 

– VRML – Export to VRML (Virtual Reality) format. For examining 

it you need a VRML viewer such as Cortona [29] or (older) Cosmo 

player [30]. 



– MDL MOL file – Export to MDL Molfile format. You need Chime 

plugin (Chemscape Chime) for Netscape to explore it [51]. 

• Options – EPS, SVG, X3D and VRML default options (see section on Exports 

to EPS/SVG/X3D/VRML). 

• Append to Pajek project file – Add current network to the end of selected 

project file (used by program PajekToSvgAnim). 

4.11 Spin 

– Select file – Select project file. 

– Append – Append to project file. 

• Spin around – Spin network around selected normal. 

• Perspective – Distant vertices are drawn smaller (or not). 

• Normal – Normal vector to spin around. 

• Step in degrees – Step in degrees when showing rotation. 

4.12 Move 

Give additional constraints on hand vertex moving: 

• Fix – Fix (do not allow) moving in x or y direction, or do not allow changing 

distance from center (circulating). 

• Grid – Define (x, y) positions on grid, these become feasible positions for 

vertices during moving by hand. 

• Circle – Define (x, y) positions on concentric circles, these become feasible 

positions for vertices during moving by hand. 

• Grasp – Determine which additional vertices are moving when clicking 

with left mouse button close to vertex in given class. Vertices that will be 

moved are in the: 

1. Closest Class Only 

2. Closest Class and Higher 

3. Closest Class and Lower 



4.13 Info 

– Select aesthetic properties of the current layout to compute: 

• Closest Vertices 

• Smallest Angle 

• Shortest/Longest Line 

• Number of crossings if lines 

• Vertex Closest to Line 

• All Properties 

Remember that coordinates of vertices must be between 0 and 1! 


Exports to EPS/SVG/X3D/VRML 69 

5 Exports to EPS/SVG/X3D/VRML 

5.1 Defaults 

If you have no labels in Draw window when you call Export there will also be no 

labels in EPS/SVG picture, otherwise numbers/labels like in Draw window will 

be shown. If you are looking at the picture using Draw/Partition, the same colors 

will be automatically used in EPS/SVG picture too. 

5.2 Parameters in EPS, SVG, X3D, and VRML Defaults Window 

Window is divided into 5 frames, two on the left and three on the right. 

Note that settings you made in this window are overwritten if the parameters 

are specified in Pajek input (NET) file. 

Top frame on the left – EPS/SVG Vertex Default 

This frame defines default drawing of vertices when we export layouts to EPS and 

SVG: 

• Interior Color – interior color of vertices (see Figure 19, page 89). If 

drawing using Partition is used, partition colors will overwrite the specified 

interior color. 

• Border Color – color of the borderline of vertices. 

• Label Color – color of label of vertices. 

• Border Width – width of the borderline of vertices. 

• Label Position: Radius /Angle – position where the label will be displayed: 

– Radius – distance of beginning of vertex label from vertex center – 

first polar parameter. 

– Angle – position of vertex label in degrees - second polar parameter 

(0..360). 

If radius is equal to 0, the label will be centered, otherwise it will be left 

aligned on the specified position. 

• Fontsize – size of font of vertices labels. 



• Label Angle – angle in which vertex labels will be displayed: if angle is 

smaller than 360, it means relative according to horizontal line (0 – horizontally); 

otherwise it is relative to center of the layout (360 – concentrically). 

The latter is useful when all vertices are drawn in concentric circle(s) using 

Layout/Circular. 

• x/y Ratio – ratio between size of vertex in x and y direction (e.g., value 1 

for circle, value larger/smaller than 1 for ellipse). 

• Shape – default shape of vertex (ellipse, box, or diamond). 

• Shapes file – default shapes file, double click to change it. 

• Export options overwrite shapes file – if checked: options selected in this 

window overwrite options defined in shapes file, otherwise default values 

for each shape are defined in selected shapes file. 

Bottom frame on the left – EPS/SVG Line Default 

This frame defines default drawing of lines when we export layouts to EPS and 

SVG: 

• Edge Color – color of edges. 

• Edge Width – width of edges. 

• Arc Color – color of arcs. 

• Arc Width – width of arcs. 

• Pattern – pattern for drawing lines (Solid or Dots). 

• Arrow Size – size of arrows. 

• Arrow Position – distance of arrow from terminal vertex: If distance is 

between 0 and 1, it means relative distance according to arc length, e.g.: 0 – 

arrow touching the terminal vertex; 0.5 – arrow in the middle of the arc. If 

distance is larger than 1 it means absolute distance from the terminal vertex 

(this is useful if you want to have all arcs on the same distance from terminal 

vertex, regardless of arcs length) 

• Label Color – color of line labels. 

• Label Angle – angle in which label of line will be displayed: if angle is 

smaller than 360, it means relative to direction of line (0 – parallel to line); 

otherwise it is relative to horizontal line (360 – horizontally). 



• Label Position – position of the center of line label – position is point on 

the line - distance of the center of line label from terminal vertex (see also 

Arrow Position) 

• Fontsize – size of font of line labels. 

• Label Position: Radius /Angle – position where the center of line label 

will be displayed according (relative) to Label Position: 

– Radius – distance of center of line label from point defined by Label 

Position - first polar parameter. 

– Angle – position of label in degrees - second polar parameter (0..360). 

• Only straight lines – drawing bidireced and multiple lines without curves. 

Top frame on the right 

This frame defines some additional defaults when we export layouts to EPS, SVG, 

X3D, or VRML: 

• EPS, SVG, X3D, VRML Size of Vertices – default size of vertices when 

exporting to X3D/VRML (valid for EPS and SVG exports as well). 

• X3D/VRML Size of Lines – width of lines in X3D/VRML. 

• EPS: Use RGB colors instead of CMYK – in description of colors in EPS 

file RGB is used (default is CMYK). 

• SVG: 3D Effect on Vertices – if selected, gradient will be applied to get 

3D look of vertices. 

Middle frame on the right – Background Colors 

This frame defines background color when exporting to EPS/SVG/X3D/VRML 

and gradients (continuously smooth color transitions from one color to another) 

when exporting layouts to SVG/X3D: 

• Bckg. Color 1 – Background color for layout in EPS/SVG/X3D/VRML. 

• Bckg. Color 2 – the second color for SVG/X3D export. No – means without 

second color, otherwise selected gradient will be used. 

• Bckg. Color 3 – the third color for SVG/X3D export – gradient. 

• Gradients – type of gradient to use in SVG (No, Linear, or Radial). In X3D 

only Radial gradient is supported. 



Bottom frame on the right 

This frame defines some additional defaults when we export layouts to EPS: 

• Left, Right, Top, Bottom – additional border around layout when exporting 

to EPS (only when EPS Clip format is selected) 

• Border Color – color of borderline of layout. It is used for export to SVG 

as well. No – means without borderline. 

• Border Radius – radius of borderline of layout (if greater than 0 it means 

oval instead of rectangle). 

• Border Width – width of borderline of layout. 

Figure 17: Spider / Kriˇzevec; Photo: Stana. 



5.3 Exporting pictures to EPS/SVG – defining parameters in 

input file 

Definition of Network (and its picture) on Input ASCII File 

For every vertex and line we can specify in details how it should be drawn (colors, 

shapes, sizes, patterns, rotations, widths...). 

A kind of standardized language is used for describing networks. The following 

reserved words are used: 

1. *Vertices n – definition of vertices follows. n is number of vertices. Each 

vertex is described using following description line: 

vertex num label [x y z] [shape] [changes of default parameters] 

Explanation: 

• vertex num – vertex number (1, 2, 3 . . . n) 

• label – if label starts with character A..Z or 0..9 first blank determines 

end of the label (e.g., vertex1), labels consisting of more words must 

be enclosed in pair of special characters (e.g., ”vertex 1”) 

• x, y, z – coordinates of vertex (between 0 and 1) 

• shape – shape of object which represents vertex. Shapes are defined 

in file SHAPES.CFG (ellipse, box, diamond, triangle, cross, empty) 

Description of parameters in shapes.cfg: 

– SHAPE s – s is external name of vertex (used in Pajek network 

file) 

– sh – sh can be ellipse, box, diamond, triangle, cross, empty. This 

is the name of PostScript procedure that actually draws object 

(procedure is defined in drawnet.pro). 

– s size – default size 

– x fact – magnification in x direction 

– y fact – magnification in y direction 

– phi – rotation in degrees of object in + direction (0..360) 

– r – parameter used for rectangle and diamond for describing radius 

of corners (r = 0 – rectangle, r > 0 – roundangle) 

– q – parameter used for diamonds – ratio between top and middle 

side of diamond (try q 0.01, q 0.5, q 2, ...) 

– ic – interior color of vertex. See Figure 19, page 89 for the list of 

possible colors. 

– bc – boundary color of vertex 



– bw – boundary width of vertex 

– lc – label color 

– la – label angle in degrees (0..360) 

– lr – distance of beginning of vertex label from vertex center (radius 

– first polar parameter) 

– lphi – position of label in degrees (0..360) (angle phi – second 

polar parameter) 

– fos – font size 

– font – PostScript font used for writing labels (Helvetica, Courier, 

...) 

– HOOKS – positions where edges can join the selected shape - according 

to s size. Three different ways to specify these positions: 

(a) CART – x y – positions in Cartesian coordinates (x,y) 

(b) POLAR – r phi – positions in polar coordinates, phi is positive 

angle (0..360) 

(c) CIRC – r phi1 – iteration of positions in polar coordinates r 

– radius, phi = k ∗ phi1, k = 1, 2, ..; k ∗ phi1 ≤ 360 

Default values can be changed for each vertex in definition line, example: 

1 ”vertex one” 0.3456 0.1234 0.5 box ic White fos 20 

Explanation: White box will represent vertex 1, label (vertex one) will be 

displayed using font size 20. 

2. *Arcs (or *Edges) – definition of arcs (edges). Format: 

v1 v2 value [additional parameters] 

Explanation: 

• v1 – initial vertex number 

• v2 – terminal vertex number 

• value – value of arc from v1 to v2 

These three parameters must always be present. If no other parameter is 

specified, the default arc will be black, straight, solid arc with following 

exceptions: 

• if value is negative, dotted line will be used instead of solid, 

• if arc is a loop (arc to itself) bezier loop will be drawn, 

• if bidirected arc exists two curved bezier arcs will be drawn. 



Arrow will be drawn at the end of the edge (at terminal vertex). 

As we mentioned, hooks are used to specify exact position where line joins 

vertices. 

Additional parameters: 

• w – width of line 

• c – color of line 

• p – pattern of line (Solid, Dots) 

• s – size of arrow 

• a – type (shape) of arrow (A or B) 

• ap – position of arrow 

– ap = 0 – arrow at terminal vertex 

– 0 < ap ≤ 1 – proportional distance from terminal vertex (according 

to line length) 

– ap > 1 – absolute distance 

• l – line label (e.g. ”line 1 2”) 

• lp – label position (look at ap) 

• lr – label radius (position of center text from point on edge ) 

• lphi – label radius (angle of center text according to point on edge ) (lr 

and lphi are polar coordinates) 

• lc – label color 

• la – label angle 

(0 < la < 360 – relative to edge, la ≥ 360 – absolute angle according 

to x axis) 

• fos – font size of label 

• font – PostScript font used for writing labels (Helvetica, Courier, ...) 

• h1 – hook at initial vertex (0 – center, -1 the closest, 1, 2.. user defined) 

• h2 – hook at terminal vertex 

• a1 – angle at initial vertex (Bezier) 

• k1 – velocity at initial vertex (Bezier) 

• k2 – velocity at terminal vertex (Bezier) 

• a2 – angle at terminal vertex (Bezier) 



Special shapes of lines can be defined using combinations of alpha1, k1, 

alpha2, k2: 

• alpha1 = alpha2 = 0, k1 ≥ 0, k2 ≥ 0 – straight line (default) 

• alpha1 = alpha2 = 0, k1 = −1, k2 > 0 – oval edge with radius k2 

(measure of radius is absolute as explained above) 

• alpha1 = alpha2 = 0, k1 = −1, k2 < 0 – second possible oval edge 

with radius −k2 

• alpha1 = alpha2 = 0, k1 = −2, k2 > 0 – circular arc with radius k2 

in positive direction 

• alpha1 = alpha2 = 0, k1 = −2, k2 < 0 – second possible circular 

arc with radius −k2 in positive direction 

• alpha1 = alpha2 = 0, k1 = −3, k2 > 0 – circular arc with radius k2 

in negative direction 

• alpha1 = alpha2 = 0, k1 = −3, k2 < 0 – second possible circular 

arc with radius −k2 in negative direction 

• alpha1 = alpha2 = 0, k1 = −4 – double edge 

• alpha1 or alpha2 �= 0, k1 > 0, k2 > 0 – Bezier curve (if alpha1 

and alpha2 have different signs line goes from one to another side of 

straight line connecting both vertices, if alpha1 and alpha2 have the 

same sign – line stays on the same side of straight line connecting both 

vertices) 

3. *Edges – definition of edges. 

The same parameters as for arcs can be used, except that type (a), size (s) 

and position (ap) have no meaning for edges. 

PS and EPS 

• PS – Export to Postscript (.PS) without header (drawnet.pro). Use it to spare 

space, if you have many pictures and your word processor enables you to 

define the header separately (like in L ATEX). 

• EPS – Export into file with Encapsulated PostScript description (.EPS). 

Drawnet.pro is already inserted in the beginning. The picture is complete, 

you can include it into text, make it bigger or smaller (without losing quality), 

rotate it, print it on Postscript printer, view it with GhostScript viewer, 

convert it to PDF, JPG... 



An example 

*Vertices 4 

1 "ellipse" 0.120 0.285 0.5 ellipse x_fact 5 y_fact 3 fos 20 ic LightYellow lc Red 

2 "box" 0.818 0.246 0.5 box x_fact 5 y_fact 3 fos 20 ic LightCyan lc Blue 

3 "diamond" 0.368 0.779 0.5 diamond x_fact 7 y_fact 3 fos 20 ic LightGreen lc Black 

4 "triangle" 0.835 0.833 0.5 triangle x_fact 9 y_fact 3 fos 20 ic LightOrange lc Brown lr 30 lphi 200 

*Arcs 

1 1 1 h2 0 w 3 c Blue s 2 a1 -130 k1 0.6 a2 -130 k2 0.6 ap 0.25 l "Bezier loop" lc OliveGreen fos 20 lr 13 lp 0.5 la 360 

2 1 1 h2 1 a1 120 k1 1 a2 10 k2 0.8 ap 0 l "Bezier arc" lphi 270 la 180 lr 13 lp 0.5 

1 2 1 h2 -1 a1 40 k1 2 a2 -30 k2 0.8 ap 0 l "Bezier arc" lphi 90 la 0 lp 0.75 

4 2 -1 l "Straight dotted arc" p Dots c Red 

*Edges 

1 3 1 l "Straight edge" lp 0.4 

3 4 1 l "Straight edge" 

You have to set some options in Pajek’s draw window: for example 

Options / Lines / Mark Lines / with labels 

to activate the display of line labels. 

Bezier loop 

ellipse 

Bezier arc 

Straight edge 

diamond 

Bezier arc 

Straight edge 

Figure 18: Example picture 

5.4 Using Unicode in Pajek’s pictures 

Straight dotted arc 

box 

triangle 

Sometimes we would like to use in Pajek’s picture some characters from unusual 

alphabets (special symbols, Cyrillic, Greek, Arabic, Chinese, ...). They are available 

in Unicode. Pajek supports Unicode UTF8 files with BOM from version 2.00 

on. 



Some hints on using Unicode in Pajek: 

• Using the free Unicode editor BabelPad we prepare the Unicode version 

of the *.NET file. Use the U tool (Unicode table) to enter the Unicode 

characters. 

• Using the BabelPad option File/Save as/UTF8 and checking Byte 

Order Mark you save network in a Unicode file. 

You can use also File/Save as/ASCII plus decimal NCR. In 

this way we transform Unicode file into an ASCII file in which the Unicode 

characters are represented using numeric codes &#dddd;. 

Any of the two files generated can be read by Pajek and proper Unicode 

characters will appear in Draw, Report and other windows provided that you 

select proper proportional and monospaced font in Options/Select 

Font in Pajek Main menu. We suggest to use Arial Unicode MS or 

Lucida Sans Unicode (one of them usually comes with Windows) for 

proportional font and GNU Unifont for monospaced font. Courier New 

can be used too. 

When saving networks they are stored as ASCII files by default (nonASCII 

characters are stored as &#dddd;) unless you check Options/Read-Write/Save 

Files as Unicode UTF8 with BOM. 

The file is used in Pajek 2.00 (or higher) to produce picture. The picture is 

exported in the SVG format. 


ανδρει 

يﺮﻴﺨﺒﺘﺼﻛ 

צעשהגלז 

Vlado 

♔♕♖♗♘♙ 

焹焓燝牕犫獨 

∰∈∀≋∞⊚ 

गङथफञऑक 

⑤⑨④②⑦ 

Андреј 


ανδρει 

يﺮﻴﺨﺒﺘﺼﻛ 

צעשהגלז 

Vlado 

♔♕♖♗♘♙ 

焹焓燝牕犫獨 

∰∈∀≋∞⊚ 

गङथफञऑक 

⑤⑨④②⑦ 

Андреј 

• The SVG picture can be opened in the free drawing program InkScape. 

Here we can make some additional enhancements of the picture. 



• In InkScape we can, using the option File/Save as/pdf or eps, save 

the picture in the desired format PDF or EPS or some other) with labels containing 

Unicode characters. Note that the PDF (1.4 or higher) also supports 

the transparency. The EPS file can be inserted in Word document. 

A set of example files is available in ZIP. 

Similar approach can be used also for 3D models in X3D. For their inspection 

we recommend the use of Instant Player. 


80 Using Macros in Pajek 


6.1 What is a Macro? 

A macro enables you to record a sequence of primitive Pajek commands into a 

file. You can use this file later to execute the saved sequence of commands without 

selecting one by one. 

6.2 How to record a Macro? 

1. First load all objects (networks, partitions,...) which will be used by a 

macro. 

2. Select objects which will be used in macro (for example, network which 

will be first used must be shown in Network ComboBox). 

3. Choose Macro/Record and select the name of macro file (default extension 

is .mcr). 

4. Use Pajek as usual to define a sequence of commands. We advise to 

add additional comments to macro file using Macro/Add Message. When 

running macro this comments are displayed in Report window and help you 

to follow the macro execution. 

5. At the end select Macro/Record again to stop recording. 

6.3 How to execute the Macro? 

1. First load object(s) that will be used as input in macro execution. 

2. Choose Macro/Play and select the macro file. 

6.4 Example 

The following macro performs topological sort of an acyclic network: 

NETBEGIN 2 

CLUBEGIN 1 

PERBEGIN 1 

CLSBEGIN 1 

HIEBEGIN 1 

VECBEGIN 1 

NETPARAM 1 


Using Macros in Pajek 81 

Msg Depth Partition 

C 1 DEP 1 (10) 

Msg Make Permutation 

P 1 MPER 1 (10) 

Msg Reordering network 

N 2 REOR 1 1 (10) 

The first seven commands store the current state of ComboBoxes. The acyclic 

network on which we want to execute topological sort must be at the top of Network 

ComboBox before starting the macro. 

6.5 List of macros available in installation file 

6.5.1 Macros prepared for genealogies and other acyclic networks 

• Path – find shortest chain (undirected path) between the two vertices. 

• Descendants – find all vertices ’later’ than selected vertex (in a p-graph). 

• Ancestors – find all vertices ’before’ the selected vertex (in a p-graph). 

• Cognatic3 – find vertices three generations ’before’ and three generations 

’after’ the selected vertex (in a p-graph). 

• Cognatic – find all reachable vertices ’before’ and all ’after’ the selected 

vertex (in a p-graph). 

• Layers, Layers1, Layers2 – draw acyclic network in layers (different algorithms). 

• zLayers – draw acyclic network in layers in z direction. 

• LongestPatrilineage – find the longest patrilineage in Ore-genealogy. The 

genealogy must be read with the option Ore graph: 1-Male, 2-Female 

links checked. 

• LongestMatrilineage – find the longest matrilineage in Ore-genealogy. The 

genealogy must be read with the option Ore graph: 1-Male, 2-Female 

links checked. 

• NumDescendants – for each vertex compute the size of output domain 

(number of descendants in Ore-graph). 

• NumAncestors – for each vertex compute the size of input domain (number 

of ancestors in Ore-graph). 



6.5.2 Macros prepared for computing derived kinship relations 

Pajek generates three relations when reading genealogy as Ore graph with the 

option Ore graph: 1-Male, 2-Female links checked: 

1 : is a father of 

2 : is a mother of 

3 : is a spouse of 

Other kinship relations can be obtained from these relations by running macros. 

Gender partition is also result of reading genealogy and is input to the following 

macros. 

4 : is a parent of 

5 : is a child of 

6 : is a son of 

7 : is a daughter of 

8 : is a husband of 

9 : is a wife of 

10 : is a sibling of 

11 : is a brother of 

12 : is a sister of 

13 : is an uncle of 

14 : is an aunt of 

15 : is a semisibling of 

Using macro add all relations you can add all above relations at once. 

As a test/example file you can use */pajek/data/family.ged 

6.6 Repeating last command 

Macro submenu enables to run the last command executed by Pajek several times 

applied to different successive objects, as well. 

Example: after loading 100 networks in Pajek, execute degree partition on 

the first network and run Repeat Last Command by typing 99 to compute degree 

partition on all other networks. 

Commands that include several objects can be run as well (e.g. extracting subnetworks 

according to selected partition(s)). There are 3 different possibilities for 

extracting from the set of networks (possibilities are selected by fixing appropriate 

objects): 

• for all networks extracting is determined by the same partition (incrementing 

applied to network, not applied to partition – partition is fixed) 


Using Macros in Pajek 83 

• for all networks extracting is determined by another partition (incrementing 

applied to network and to partition – nothing is fixed) 

• for one network several extractions are determined by different partitions 

(incrementing not applied to network, applied to partition – network is 

fixed) 

Important: Always first execute the command on the first loaded object(s). 

Repeating will start with object(s) that have object number(s) one higher than the 

object(s) on which the command was executed. 

If the result of the command is also a constant, all constants are stored in a 

vector. In Pajek the following constants exist: number of vertices, arcs, edges, 

network densities, centralization indices, diameter, relinking index, correlation 

and contingency coefficients, number of fragments, main core number, number 

of components, length of critical path, maximum flow, distance between vertices, 

number of islands, minimum and maximum value in partition / hierarchy, minimum, 

maximum, arithmetic mean, median and standard deviation in vector. 


84 Blockmodeling in Pajek 


The blockmodeling option is an embedding of the programs for optimization approach 

to generalized blockmodeling MODEL2 and TwoMODEL from package 

STRAN – STRucture ANalysis [9] into Pajek. 

The blockmodeling command seeks for the best partition of a given network 

satisfying given types of blocks – generalized blockmodeling [7, 35]. The blockmodel 

can be built inside Pajek (if User Defined is selected) and/or its description 

can be stored in MDL file. The impact of errors in each block can be controlled 

using penalty weights. 

The option supports also generalized blockmodeling of two-mode networks 

[34]. 

The maximum size of a network on which the command can be applied is 250 

vertices. But the real limit is time complexity – already on 100 vertices optimization 

can last some hours. 

The results of the command are stored as partitions. They can be displayed as 

a picture 

Draw / Draw-Partition 

and 

Layout / Energy / Kamada-Kawai / Free 

or 

Layout / Circular / using Partition 

The result can be displayed also in the matrix form. This requires two steps: 

Partition / Make Permutation 

File / Network / Export Matrix to EPS / 

Using Permutation enter file name; yes 

7.1 MDL files 

The structure of a MDL file is evident from the following example 

*MODEL Tina 

9 

0 3 100 0 1 2 3 4 

*CONSTRAINTS 

1 100 2 1 

4 100 1 3 

*EOM 

The first character in each line should be a star * or a blank. 

The last character in a line should not be a blank. 


Blockmodeling in Pajek 85 

A number in the second line is number of clusters. In the case of two-mode 

network two numbers should be given in this line – number of row-clusters and 

number of col-clusters. The other data are the same for both type of networks. 

The following lines have the structure 

i j penalty t1 t2 . . . tk 

When i, j > 0 the line prescribes that the block (i, j) can be of types t1, t2 . . . tk. 

The types are coded as follows 

0 - - null 7 rfn - row-function 

1 com - complete 8 cfn - col-function 

2 rdo - row-dominant 9 den - density 

3 cdo - col-dominant 10 dnc - do not care 

4 reg - regular 11 one - non-null 

5 rre - row-regular 12 sym - symmetric 

6 cre - col-regular 

Lines with i = 0 defines the types of of parts of model matrix: 

• j = 0: diagonal (for one-mode networks only); 

• j = 1: upper triangle (for one-mode networks only); 

• j = 2: lower triangle (for one-mode networks only); 

• j = 3: complete matrix. 

In the case of several lines describing the same block the last prescription 

prevails. 

Lines following *CONSTRAINTS define additional constraints in blockmodel. 

Constraints have the form 

k penalty i j 

with the following meaning 

• k = 1: i ∈ Cj – vertex i belongs to cluster Cj; 

• k = 2: i /∈ Cj – vertex i does not belong to cluster Cj; 

• k = 3: C(i) = C(j) – vertices i and j belong to the same cluster; 

• k = 4: C(i) �= C(j) – vertices i and j belong to different clusters; 

• k = 5: i ≤ |C(j)| – cluster Cj contains at least i vertices; 



• k = 6: i ≥ |C(j)| – cluster Cj contains at most i vertices. 

Be careful in the case of two mode network for constraints of type k = 5 and 

k = 6 (constraints on min/max number of vertices in selected cluster): If there 

are r row-clusters and c col-clusters in blockmodel, then use numbers in the range 

1 . . . r to define constraint on row-cluster and numbers in the range r + 1 . . . r + c 

to define constraint on col-cluster. 

The violations of constraints contribute to criterion function with a term 

+ # of violations × penalty 

The values of penalties have to be in the range 0 to 1000. 

7.2 Examples of MDL files 

7.2.1 Regular blocks 

*MODEL Regular 

10 

0 3 1 0 1 4 

*EOM 

7.2.2 Diagonal blocks (clustering) 

*MODEL Diagonal 

10 

0 3 100 0 

0 0 1 0 1 4 

*EOM 

7.2.3 Acyclic model (up) 

*MODEL Hierarchy 

9 

0 1 1 0 5 6 

0 0 10 0 1 4 12 

0 2 100 0 

*EOM 

7.2.4 Acyclic model with symmetric clusters (down) 

*MODEL SymHiera 

9 


Blockmodeling in Pajek 87 

0 0 10 0 1 12 

0 1 100 0 

0 2 1 0 11 

*EOM 

7.2.5 Center-Periphery 

*MODEL Center-Periphery 

2 

0 3 1 0 11 

2 2 10 0 

1 1 100 0 1 4 

*EOM 

7.2.6 Regular path 

*MODEL Regular Path 

9 

0 0 10 0 1 4 

1 2 10 0 1 4 

2 3 10 0 1 4 

3 4 10 0 1 4 

4 5 10 0 1 4 

5 6 10 0 1 4 

6 7 10 0 1 4 

7 8 10 0 1 4 

8 9 10 0 1 4 

*EOM 

7.2.7 Regular chain 

*MODEL Regular Chain 

9 

0 0 10 0 1 4 

1 2 10 0 1 4 

2 3 10 0 1 4 

3 4 10 0 1 4 

4 5 10 0 1 4 

5 6 10 0 1 4 

6 7 10 0 1 4 

7 8 10 0 1 4 



8 9 10 0 1 4 

2 1 10 0 1 4 

3 2 10 0 1 4 

4 3 10 0 1 4 

5 4 10 0 1 4 

6 5 10 0 1 4 

7 6 10 0 1 4 

8 7 10 0 1 4 

9 8 10 0 1 4 

*EOM 

7.2.8 2-mode ’standard model’ for Davis.net 

*MODEL UserDefined 

2 3 

1 1 1 1 

1 2 1 1 

1 3 100 0 

2 1 100 0 

2 2 1 1 

2 3 1 1 

*EOM 


Colors in Pajek 89 

8 Colors in Pajek 

GreenYellow 

Yellow 

Goldenrod 

Dandelion 

Apricot 

Peach 

Melon 

YellowOrange 

Orange 

BurntOrange 

Bittersweet 

RedOrange 

Mahogany 

Maroon 

BrickRed 

Red 

OrangeRed 

RubineRed 

WildStrawberry 

Salmon 

CarnationPink 

Magenta 

VioletRed 

Rhodamine 

Mulberry 

RedViolet 

Fuchsia 

Lavender 

Thistle 

Orchid 

DarkOrchid 

Purple 

Plum 

Violet 

RoyalPurple 

BlueViolet 

Periwinkle 

CadetBlue 

CornflowerBlue 

MidnightBlue 

NavyBlue 

RoyalBlue 

Blue 

Cerulean 

Cyan 

ProcessBlue 

SkyBlue 

Turquoise 

TealBlue 

Aquamarine 

BlueGreen 

Emerald 

JungleGreen 

SeaGreen 

Green 

ForestGreen 

PineGreen 

LimeGreen 

YellowGreen 

SpringGreen 

OliveGreen 

RawSienna 

Sepia 

Brown 

Tan 

Gray 

Black 

White 

LightYellow 

LightCyan 

LightMagenta 

LightPurple 

LightGreen 

LightOrange 

Canary 

LFadedGreen 

Pink 

LSkyBlue 

Gray05 Gray10 Gray15 






Figure 19: Colors in Pajek. 


90 Colors in Pajek 

0 - Cyan 

1 - Yellow 

2 - LimeGreen 

3 - Red 

4 - Blue 

5 - Pink 

6 - White 

7 - Orange 

8 - Purple 

9 - CadetBlue 

10 - TealBlue 

11 - OliveGreen 

12 - Gray 

13 - Black 

14 - Maroon 

15 - LightGreen 

16 - LightYellow 

17 - Magenta 

18 - MidnightBlue 

19 - Dandelion 

Figure 20: Partition colors. 

20 - WildStrawberry 

21 - ForestGreen 

22 - Salmon 

23 - LSkyBlue 

24 - GreenYellow 

25 - Lavender 

26 - LFadedGreen 

27 - LightPurple 

28 - CornflowerBlue 

29 - LightOrange 

30 - Tan 

31 - LightCyan 

32 - Gray20 

33 - Gray60 

34 - Gray40 

35 - Gray75 

36 - Gray10 

37 - Gray85 

38 - Gray30 

39 - Gray70 


Citing Pajek 91 

9 Citing Pajek 

For citing Pajek you may consider: 

• V. Batagelj, A. Mrvar: Pajek – Program for Large Network Analysis. 

Home page: http://vlado.fmf.uni-lj.si/pub/networks/pajek/ 

• W. de Nooy, A. Mrvar, V. Batagelj: Exploratory Social Network Analysis 

with Pajek, Structural Analysis in the Social Sciences 27, Cambridge University 

Press, 2005. ISBN:0521602629. CUP, Amazon. 

• V. Batagelj, A. Mrvar: Pajek – Analysis and Visualization of Large Networks. 

In Jünger, M., Mutzel, P. (Eds.): Graph Drawing Software. Springer 

(series Mathematics and Visualization), Berlin 2003. 77-103. ISBN 3-540- 

00881-0. Springer, Amazon, preprint 

• V. Batagelj, A. Mrvar: Pajek – Program for Large Network Analysis. Connections, 

21(1998)2, 47-57. preprint 

Figure 21: Gartenkreuzspinne / Araneus diadematus; Photo: Stefan Ernst 


92 References 

References 

[1] Adobe SVG viewer. http://www.adobe.com/svg/ 

http://www.adobe.com/svg/viewer/install 

[2] Ahmed, A., Batagelj, V., Fu, X., Hong, S.-H., Merrick, D., Mrvar, A. (2007): 

Visualisation and analysis of the Internet movie database. Asia-Pacific Symposium 

on Visualisation 2007 (IEEE Cat. No. 07EX1615), 17-24. 

[3] Albert R., Barabasi A.L.: Topology of evolving networks: local events and 

universality. 

http://xxx.lanl.gov/abs/cond-mat/0005085 

[4] Batagelj V.: Papers on network analysis. 

http://vlado.fmf.uni-lj.si/pub/networks/doc/ 

[5] Batagelj V.: Workshop on Network Analysis, Sydney, Australia: 14th to 

17th June 2005; at Nicta (National ICT Australia). 

http://vlado.fmf.uni-lj.si/pub/networks/doc/#NICTA 

[6] Batagelj V.: Some new procedures in Pajek. Dagstuhl seminar 05361, 

Dagstuhl, Germany, Sept 5-9, 2005. 

http://vlado.fmf.uni-lj.si/pub/networks/doc/dagstuhl/NewProcs.pdf 

[7] Batagelj, V. (1997) Notes on blockmodeling. Social Networks 19, 143-155. 

[8] Batagelj V.: Efficient Algorithms for Citation Network Analysis. 

http://arxiv.org/abs/cs.DL/0309023 

[9] Batagelj V.: MODEL 2. http://vlado.fmf.uni-lj.si/pub/networks/ 

[10] Batagelj V. (2009): Social Network Analysis, Large-Scale. R.A. Meyers, ed., 

Encyclopedia of Complexity and Systems Science, Springer 2009: 8245- 

8265. http://www.springerlink.com/content/tp3w7237m4624462/ 

[11] Batagelj V. (2009): Complex Networks, Visualization of. R.A. Meyers, ed., 

Encyclopedia of Complexity and Systems Science, Springer 2009: 1253- 

1268. http://www.springerlink.com/content/m472707688618h17/ 

[12] Batagelj V., Brandes U. (2005): Efficient Generation of Large Random Networks. 

Physical Review E 71, 036113, 1-5. 

[13] Batagelj, V., Ferligoj, A., and Doreian, P. (1992), Direct and Indirect Methods 

for Structural Equivalence, Social Networks, 14, 63–90. 


References 93 

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to Regular Equivalence. Social Networks 14, 121-135. 

[15] Batagelj, V, Ferligoj, A, Doreian, P (2007): Indirect blockmodeling of 3-way 

networks. Selected contributions in data analysis and classification, Springer, 

Berlin, 151-159. 

[16] Batagelj, V., Kejˇzar, N., Korenjak-Černe, S. (2008): Analysis of the Customers? 

Choice Networks: An Application on Amazon Books and CDs 

Data. Metodoloˇski zvezki/Advances in Methodology and Statistics 4 (2): 

191-204. 

[17] Batagelj V., Mrvar A.: Pajek. 

http://vlado.fmf.uni-lj.si/pub/networks/pajek/ 

[18] Batagelj V., Mrvar A. (2000) Some Analyses of Erdős Collaboration Graph. 

Social Networks, 22, 173-186 

[19] Batagelj V., Mrvar A. (2001) A Subquadratic Triad Census Algorithm for 

Large Sparse Networks with Small Maximum Degree. Social Networks, 23, 

237-243 

[20] Batagelj V., Mrvar A. (2008) Analysis of Kinship Relations With Pajek. Social 

Science Computer Review 26(2), 224-246, 2008. 

[21] Batagelj V., Mrvar A., Zaverˇsnik M. (1999) Partitioning Approach to Visualization 

of Large Graphs. In: Kratochvil J. (Ed.) GD’99, ˇStiˇrin Castle, Czech 

Republic. LNCS 1731. Springer-Verlag, 90-97. 

[22] Batagelj V., Mrvar A., Zaverˇsnik M. (2002) Network analysis of texts. Language 

Technologies, Ljubljana, p. 143-148. 

http://nl.ijs.si/isjt02/zbornik/sdjt02-24bbatagelj.pdf 

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Springer 

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Math 307 (3-5): 310-318. 

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Social Networks, 18. 149-168 

[33] Doreian, P., Batagelj, V., Ferligoj, A. (2000) Symmetric-acyclic decompositions 

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Analysis in the Social Sciences 25, Cambridge University Press, 2005. 

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vlasteoskog kruga pomoću programa Pajek. Anali Dubrovnik XL, HAZU, 

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[37] GEDCOM 5.5. 

http://homepages.rootsweb.com/˜pmcbride/gedcom/55gctoc.htm 

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of IFCS 2009. Studies in Classification, Data Analysis, and Knowledge 

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Pajek manual - Vladimir Batagelj

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