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

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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  1. 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

  2. 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

  3. 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

  4. 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

  5. Effect Of Interslice Weights Fadi Towfic, August 16, 2010

  6. 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

  7. 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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