“Pajek”: Large Network Analysis

1. “Pajek”: Large Network Analysis

2. Agenda • Introduction • Network Definitions • Network Data Files • Network Analysis 2

3. Introduction to Slovenian Spider: Pajek • http://vlado.fmf.uni-lj.si/pub/networks/pajek/ • Free software • Windows 32 bit • Pajek 2.05 “Whom would you choose as a friend ?” 3

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 4

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

9. Transform 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