コミュニティ&モジュラリティ

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  • &

    2011/10/21

  • 2

  • etc

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  • n-Clique, n-Clan, n-Club, k-Cores, k-Plex, k-

    CliqueCommunity, k-degenerate etc.

    k-Partition, Modularity

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  • 5

  • Question?

  • Null Model

    NewmanModularity

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    Q =v,w

    Avw2M

    P(v,w)(c(v), c(w))

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  • Null Model

    (Null hypothesis)

    Null model

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  • Modularity NewmanNull model

    vw

    NewmanModularity: Q

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    P(v,w) =d(v)2M

    d(w)2M

    Q =v,w

    Avw2M

    P(v,w)(c(v), c(w))

    x==y ? 1 : 0

    vid

    v

    A(x, y)

    c(v)

    M

    d(v)

  • Modularity

    Bell Number Modularity

    Divisive Permutation of Maximal Edge Betweenness Eigenvector Leading Partition from Modularity Matrix Extremal Optimization for Modularity

    Agglomerative Combining A Community Pair which Maximize Modularity Label Propagation for Modularity Size Reduction and Repeatedly Moving Communities

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  • Choosing null model problems Resolution limit in community detection Significance of community

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