Tutorial 3 Pajek basics Qi YU Getting started

Tutorial 3: Pajek basics Qi YU

§ Getting started § Data format in Pajek § Window tools in Pajek § Resources

§ 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.

§ 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/

Approaches to deal with large networks

§ 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.

§ Getting started § Data format in Pajek § Window tools in Pajek § Resources

§ 1. network – main object (vertices and lines - arcs, edges): § - graph, valued network, multirelational, 2 -mode or temporal network § 2. partition § - they tell for each vertex to which class vertex belong. Default extension: . clu § 3. vector § - they tell for each vertex some numerical property (real number). Default extension: . vec § 4. permutation – reordering of vertices § - reordering of vertices. Default extension: . per § 5. cluster § - subset of vertices (e. g. one class from partition). Default extension: . cls. § 6. hierarchy § - hierarchically vertices. Default extension: . hie

§ Network can be defined in different ways on input file. Look at three of them: § 1. List of neighbours (Arcslist / Edgeslist)(see test 1. net) *Vertices 5 1 ”a” 2 ”b” 3 ”c” 4 ”d” 5 ”e” *Arcslist 124 23 314 45 *Edgeslist 15

§ Data must be prepared in an input (ASCII) file. Program Note. Pad can be used for editing. Much better is a shareware editor, Text. Pad. § Words, starting with *, must always be written in first column of the line. They indicate the start of a definition of vertices or lines. § Using *Vertices 5 we define a network with 5 vertices. This must always be the first statement in definition of a network. § Definition of vertices follows after that – to each vertex we give a label, which is displayed between “ and ”. § Using *Arcslist, a list of directed lines from selected vertices are declared (1 2 4 means, that there exist two lines from vertex 1, one to vertex 2 and another to vertex 4). § Similarly *Edgeslist, declares list of undirected lines from selected vertex. § In the file no empty lines are allowed – empty line means end of network.

§ 2. Pairs of lines (Arcs / Edges) (see test 2. net) *Vertices 5 1 ”a” 2 ”b” 3 ”c” 4 ”d” 5 ”e” *Arcs 121 141 232 311 342 451 *Edges 151

§ Directed lines are defined using *Arcs, undirected lines are defined using *Edges. The third number in rows defining arcs/edges gives the value of the arc/edge. § In the previous format (Arcslist / Edgeslist) values of lines cannot be defined § – the format is suitable only if all values of lines are 1. § If values of lines are not important the third number can be omitted (all lines get value 1). § In the file no empty lines are allowed – empty line means end of network.

§ 3. Matrix (see test 3. net) *Vertices 5 1 ”a” 2 ”b” 3 ”c” 4 ”d” 5 ”e” *Matrix 01011 00200 10020 00001 10000

§ In this format directed lines (arcs) are given in the matrix form (*Matrix). If we want to transform bidirected arcs to edges we can use “Net>Transform>Arcs to Edges>Bidirected only”

§ Only those elements necessary to define structure of network were described so far. Additionally, Pajek enables precise definition of elements used for drawing networks (coordinates of vertices, shapes and colors of vertices and lines, . . . ). § Example: (see test 4. net) *Vertices 5 1 “a” box 2 “b” ellipse 3 “c” diamond 4 “d” triangle 5 “e” empty. . .

§ Simple networks can be defined inside program Pajek as well without definition in an input file: § Select: “Net>Random Network>Total No. of Arcs”

§ Partitions are used to describe nominal properties of vertices. § e. g. , 1 -men, 2 -women § Definition in input file (see test. clu) *Vertices 5 1 2 2 2 1

§ We can build a partition using Pajek too: § Use "Partition>Create Null Partition”, or § Select “Draw>Draw-Select. All” § Using that command three operations are executed: § a new partition of equal dimension as the number of vertices is generated; § all vertices are put to cluster 0, and § the network is drawn using the obtained null partition (all vertices are cyan).

§ Vectors are used to describe numerical properties of vertices (e. g. , centralities). § Definition in input file (see test. net) *Vertices 5 0. 58 0. 25 0. 08 0. 25

§ Often it is the case that not only network but also several properties of the vertices are known in advance. This properties are usually stored as partitions or vectors. It is time consuming to load objects one by one. Therefore it is convenient to store all data in one file, called Pajek project file (. paj). (see test. paj) § Project files can be produced manually by using “File>Pajek Project File>Save” § To load objects stored in Pajek project file select “File>Pajek Project File>Read”

§ Getting started § Data format in Pajek § Window tools in Pajek § Resources

§ The Main screen menus have a clear logic. § Manipulations that involve one type of data object are listed under a menu with the object’s name; § For example, the Net menu contains all commands that operate on one network and the Nets menu lists operations on two networks. § Manipulations that need different kinds of objects are listed in the Operations menu. § For example, if we want to extract a sub-network that consists of men from the original network file, two kinds of files are needed, that is the original network file and the partition file in which each vertex is assigned to the class “men” or “women”. Then we should select the option “operations>extract from network>partition”

§ FILE § NET § OPERATIONS § PARTITION § VECTOR § DRAW § INFO

§ Options>Mark vertices using § selects the way vertices are marked inthe picture § Options>Lines § visibility or nonvisibiliy of arcs and edges, selects the way lines are marked in the picture § Options>Size § selects the size of vertices, size of font, size of arrows and width of lines § Options>Colors § selects background color, color of vertices, lines, font. . .

§ Getting started § Data format in Pajek § Window tools in Pajek § Resources

§ Download § The latest version of Pajek is freely available, for non-commercial use, at its home page: http: //vlado. fmf. uni-lj. si/pub/networks/pajek/ § Text file into Pajek § http: //vlado. fmf. uni-lj. si/pub/networks/pajek/howto/text 2 pajek. htm § Wo. S to Pajek § http: //vlado. fmf. uni-lj. si/pub/networks/pajek/Wo. S 2 Pajek/default. htm § Tutorial § Exploratory Social Network Analysis with Pajek § visit Pajek wiki for more information § http: //pajek. imfm. si/doku. php