“Pajek”: Large Network Analysis

2 Agenda Introduction Network Definitions Network Data Files Network Analysis 2

3 3 Introduction to Slovenian Spider: PajekSlovenian Spider: Pajek   Free software  Windows 32 bit Pajek 2.05 “Whom would you choose as a friend ?”

4 4 Introduction Its applications:  Communication networks: links among pages or servers on Internet, usage of phone calls  Transportation networks  Flow graphs of programs  Bibliographies, citation networks

5 Data Structures Six data structures:  Network(*.net) – main object (vertices and lines - arcs, edges)  Partition(*.clu) – nominal property of vertices (gender);  Vector(*.vec) – numerical property of vertices;  permutation (*.per) – reordering of vertices;  cluster (*.cls) – subset of vertices (e.g. a cluster from partition);  hierarchy (*.hie) – hierarchically ordered clusters and vertices.

6 Introduction Pajek 2.05

7 Network Definitions Graph Theory  Graphs represent the structure of networks Directed and undirected graphs  Lists of vertices arcs and edges, where each arch and edge has a value. To view the network data files: NotePad, EditPlus

8 Network Data File 8 Open Network Data File (*.net) Number of Vertices

9 Transform

10 Report Information

11 Visualization Energy – Idea: the network is represented like a physical system, and we are searching for the state with minimal energy.  Two algorithms are included: Layout/Energy/Kamada-Kawai – slower Layout/Energy/Fruchterman-Reingold – faster, drawing in a plane or space (2D or 3D), and selecting the repulsion factor

12 Network Creation 12

13 Partitions File name: *.clu

14 Degree

15 Assignment Network Building (2 or 3 Students/Group)  Random Network  Small-World Network  Scale-free Network Required Characteristics  Combination of arcs and edges  Number of vertices >100  Partition in 2 groups  In-degree and Out-degree  Information Report  Visualization