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c04_netw_commun - Community structure in networks Many...

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Community structure in networks Many real-world networks, especially social ones, exhibit community structure (also called modularity) . I t iti l it t t b d fi d th Intuitively community structure can be defined as the existence of subgraphs that are densely connected but sparsely inter-connected.
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Karate club friendship network The club later split into two. Collaborations at the S t F I tit t Santa Fe Institute
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Examples of communities Network : World Wide Web Nodes : webpages Edges : hyper-references Communities : Nodes on related topics Network : Friendship network Nodes : people Ed f i d hi Edges : friendship Communities : Group formation among people Network : Metabolic networks Nodes : metabolites Edges : participation in a chemical reaction Communities : Functional modules
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Definitions of a community Cliques (completely connected subgraphs) Chain of cliques – adjacent cliques share every node except one k-clan – diameter (largest path length) is k Definitions using the edges inside and outside a presumed community k i in – edges of node i that stay inside the community k i out
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