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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

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
Standard Evaluation of Communities Multiplex Networks

  • 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 communities1
Standard Evaluation of Communities Multiplex Networks

  • 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
Limitations Multiplex Networks

  • 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
Effect Of Interslice Weights Multiplex Networks

Fadi Towfic, August 16, 2010


Q multislice
Q Multiplex Networksmultislice

  • 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
Conclusions/Uses Multiplex Networks

  • 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