16-ncp_annot

16-ncp_annot - CS224W:SocialandInformationNetworkAnalysis

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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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on verlapping vs overlapping communities Non overlapping vs. overlapping communities 11/10/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2
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[Palla et al., ‘05] node belongs to many social circles A node belongs to many social circles 11/10/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3
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[Palla et al., ‘05] o nodes belong to the same community if they Two nodes belong to the same community if they can be connected through adjacent k cliques: k clique: Fully connected graph on k nodes djacent iques: 4-clique Adjacent k cliques: overlap in k-1 nodes k clique community Set of nodes that can be reached through a quence of adjacent adjacent 3-cliques sequence of adjacent k cliques 11/10/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4
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[Palla et al., ‘05] lique Percolation Method: Clique Percolation Method: Find maximal cliques (not k cliques!) Clique overlap matrix: Each clique is a node Connect two cliques if they verlap in at least - odes overlap in at least k 1 nodes Communities: Connected components of the clique overlap matrix How to set k ? Set k so that we get the “richest” (most widely distributed cluster sizes) community structure 11/10/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5
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[Palla et al., ‘05] Start with graph and find maximal cliques reate clique Create clique overlap matrix Threshold the (1) Graph (2) Clique overlap matrix matrix at value k 1 If a ij <k-1 set 0 ommunities are Communities are the connected components of the resholded atrix ) hresholded thresholded matrix 11/10/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6 (3)Thresholded matrix at k=4 (4) Communities (connected components)
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[Palla et al., ‘07] Communities in a “tiny” part of a phone ll tk f calls network of 4 million users [Barabasi Palla, 2007] 11/10/2010 7 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu
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ch node is a community Each node is a community Nodes are weighted for mmunity size community size Links are weighted for verlap size overlap size DIP “core” data base of protein interactions (S. cerevisiase, yeast) 11/10/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8
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o nice way NP ard combinatorial problem No nice way, NP hard combinatorial problem Simple Algorithm: art with max ique size Start with max clique size s Choose node u , extract iques of size ode cliques of size s node u is member of elete d its edges Delete u and its edges When graph is empty, s=s-1 , start on original graph
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This note was uploaded on 01/11/2011 for the course CS 224 at Stanford.

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16-ncp_annot - CS224W:SocialandInformationNetworkAnalysis

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