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