Community structure in time dependent multiscale and multiplex networks
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Community Structure In Time-Dependent, Multiscale, And Multiplex Networks. Peter J. Mucha, Thomas Richardson, Kevin Macon, Mason A. Porter, Jukka-Pekka Onnela. Science 14 May 2010: Vol. 328. no. 5980, pp. 876 - 878 DOI: 10.1126/science.1184819. Standard Evaluation of Communities.

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Community Structure In Time-Dependent, Multiscale, And Multiplex Networks

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Community Structure In Time-Dependent, Multiscale, And Multiplex Networks

Peter J. Mucha, Thomas Richardson, Kevin Macon, Mason A. Porter, Jukka-Pekka Onnela

Science 14 May 2010:Vol. 328. no. 5980, pp. 876 - 878DOI: 10.1126/science.1184819

Fadi Towfic, August 16, 2010


Standard Evaluation of Communities

  • Q = Σij (Aij − Pij) δ(gi, gj)

    • A = adjacency matrix

    • P = expected weight of edge ij under some null model

    • δ = Indicator function, 1 if gi,gj belong to same community, 0 otherwise

Fadi Towfic, August 16, 2010


Standard Evaluation of Communities

  • An equivalent way to measure communities:

    • (Number of edges connecting node i to nodes within a chosen community) – (all possible edges between node i and all other nodes in the graph)

Fadi Towfic, August 16, 2010


Limitations

  • No good null model for time-dependent graphs

  • More graphs have time-dependent components

    • social networks

    • gene-networks

    • computer networks

  • Definition of community depends on edge connectivity, how to take into account 3D?

Fadi Towfic, August 16, 2010


Effect Of Interslice Weights

Fadi Towfic, August 16, 2010


Qmultislice

  • Parameters:

  • γ is a resolution parameter [0-1]

  • 2μ number of connections possible for any node across all slices

  • kjs is strength of node j in slice s (computed as Kjs = Σi Aijs)

  • ms total sum of all strengths in slice s (computed as ms = Σj kjs)

  • δij or δsr is an indicator function = 1 if it is possible to transition from ij or sr, 0 otherwise

  • δ(gis,gjr) is an indicator function = 1 if node i in slice s is in the same community as node j in slice r.

Fadi Towfic, August 16, 2010


Conclusions/Uses

  • First evaluation measure of its kind to study community detection across time in graphs

  • Extends Laplacian dynamics

  • Can help in studying community evolution across time

    • Not a community detection algorithm!

    • Network can now be dynamic (time-based, space-based…etc) instead of static entities

    • No current application of this method in Bioinformatics

Fadi Towfic, August 16, 2010


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