14-communities_annot

14-communities_annot -...

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CS224W: Social and Information Network Analysis re eskovec tanford University Jure Leskovec, Stanford University http://cs224w.stanford.edu
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etworks of ghtly Networks of tightly connected groups Network communities: ts of nodes with ts f Sets of nodes with lots of connections inside and w utside he rest few to outside (the rest of the network) Communities, clusters, 2 groups, modules 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu
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[Onnela et al. ‘07] Edge strengths (call volume) in real network Edge betweenness in real network 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3
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[Girvan Newman PNAS ‘02] Divisive hierarchical clustering based on edge betweenness : Number of shortest paths passing through the edge irvan ewman Algorithm: Girvan Newman Algorithm: Repeat until no edges are left: Calculate betweenness of edges Remove edges with highest betweenness Connected components are communities ives a hierarchical decomposition of the network Gives a hierarchical decomposition of the network Example: 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4
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[Newman Girvan PhysRevE ‘03] chary’s Karate club: Zachary s Karate club: hierarchical decomposition 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5
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[Newman Girvan PhysRevE ‘03] 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6 Communities in physics collaborations
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Breath first search starting from A: Want to compute betweenness of paths starting at node A 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 7
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ount the number of shortest paths from A to Count the number of shortest paths from A to all other nodes of the network: 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8
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ompute etweenness y working up the tree: Compute betweenness by working up the tree: If there are multiple paths count them fractionally 1+1 paths to H Split evenly Repeat the BFS procedure for each 1+0.5 paths to J Split 1:2 node of the network Add edge scores untime (all pairs shortest path): 11/3/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 9 1 path to K Split evenly Runtime (all pairs shortest path): ‐‐ Weighted graphs: O(N 3 ) ‐‐ Unweighted graphs: O(N 2 )
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efine odularity be Define modularity to be Q = (number of edges within groups) – xpected number within groups) (expected number within groups) Actual number of edges betweeniand j is Expected number of edges between i and j is 11/3/2010 10 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu m…number of edges
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(number of edges within groups) Q = (number of edges within groups) – (expected number within groups) hen:
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This note was uploaded on 01/11/2011 for the course CS 224 at Stanford.

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14-communities_annot -...

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