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“Pajek”: Large Network Analysis
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2 Agenda Introduction Network Definitions Network Data Files Network Analysis 2
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3 3 Introduction to Slovenian Spider: PajekSlovenian 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 ?”
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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
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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.
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6 Introduction Pajek 2.05
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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
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8 Network Data File 8 Open Network Data File (*.net) Number of Vertices
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9 Transform
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10 Report Information
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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
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12 Network Creation 12
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13 Partitions File name: *.clu
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14 Degree
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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
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