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Social Network Analysis

Social Network Analysis. Dr Yi Zhou (yzhou@scm.uws.edu.au). Content. Generate Social Networks Social Network Analysis in general Agna Conclusion. Content. Generate Social Networks Social Network Analysis in general Agna Conclusion. Generate Random Graphs. N nodes

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Social Network Analysis

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  1. Social Network Analysis Dr Yi Zhou (yzhou@scm.uws.edu.au)

  2. Content • Generate Social Networks • Social Network Analysisin general • Agna • Conclusion

  3. Content • Generate Social Networks • Social Network Analysis in general • Agna • Conclusion

  4. Generate RandomGraphs Nnodes A pair of nodes has probabilitypof being connected. Average degree, k ≈ pN Given N and p, generate a randomgraph For i=1…N For j=i+1…N generate a random number 0<a<1; If a<p then E(i,j)=1 else E(i,j)=1; Is it possible to develop an algorithm to generate social networks?

  5. The AlphamodelWatts (1999) The people you know aren’t randomly chosen. People tend to get to know those who are two links away (Rapoport , 1957). The real world exhibits a lot of clustering.

  6. The AlphamodelWatts (1999) a model: Add edges to nodes, as in random graphs, but makes links more likely when two nodes have a common friend. Probability of linkage as a function of number of mutual friends (a is 0 in upper left, 1 in diagonal, and ∞ in bottom right curves.)

  7. Clustering coefficient Normalized path length Clustering coefficient (C) and average path length (L) plotted against a The AlphamodelWatts (1999) • a model: Add edges to nodes, as in random graphs, but makes links more likely when two nodes have a common friend. • For a range of a values: • The world is small (average path length is short), and • Groups tend to form (high clustering coefficient). a

  8. Other Models • The Betamodel • The Waxmanmodel • The Configurationmodel • The Copyingmodel • Many more … a

  9. SearchableNetwork Just because a short path exists, doesn’t mean you can easily find it. You don’t know all of the people whom your friends know. Under what conditions is a network searchable?

  10. Content • Generate Social Networks • Social Network Analysisin general • Agna • Conclusion

  11. What we want for SNA? • Visualization • To visualize the social network as a diagram • Overview of the graph • How big? How dense? How close? • Personal community • The subgraphs connected to a particular individual • Reachability • The shortest path between individuals

  12. What we want for SNA? • Popularity • How popular an individual is • Importance • How important an individual is • Cluster • What are the groups/communities • Many more … • e.g., which individual is acting strange

  13. Visualization

  14. Overviewof the Social Network • Size • number of nodesN • Edges • number of edgesE • Density • the ratio: number of edges/number of possible edges • (undirected graph) : 2E/N(N-1) • (directed graph without self edge) : E/N(N-1) • Diameters • The biggest number of all distances

  15. Personal Community • Given a particular individualA • The in-degree of A • number of edgescoming into A • The out-degree of A • number of edgesgoing out of A • The subgraph induced by Awithink steps • the subgraph containing A and all other individualsreachable to A with a distance no more than k

  16. Reachability • Given two individualsA and B • Reachability • whether there exists a walk from A to B • Walks • if yes, what are the possible (shortest) walks • Distance • the length of the shortest walks from A to B

  17. Popularity • Given a particular individualA • Connections • how many nodes connected to A within ksteps • Eccentricity • the maximaldistance of A to all other individuals • Closeness • the average distance of A to all other individuals

  18. Importance • Given a particular individualA • Degree • the number of edgescoming in and going out of A • Closeness • the average distance of A to all other individuals • Betweenness • the number of individual pairs (B,C), for which A lies in a shortestwalk from B to C

  19. Cluster • k-clique • A subgraph, in which every two individuals are reachable within ksteps

  20. An Example Degree of node 2: 3 Size: 8 Density: 0.286 Diameter: 4 Shortest path from 1 to 8: 1328 Eccentricity of node 2 : 2 Betweenness of node 2 : 32 Closeness of node 2 : 0.09

  21. Content • Generate Social Networks • Social Network Analysis in general • Agna • Conclusion

  22. Agna A freeSNA software

  23. Content • Generate Social Networks • Social Network Analysis in general • Agna • Conclusion

  24. Concluding Remarks • Generate Social networks using the alpha model • Social Network Analysis (SNA) • How to calculate the measurements for SNA • Agna at a glance

  25. Thank you!

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