Peter J. Mucha, Thomas Richardson, Kevin Macon, Mason A

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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 Name, affliation, why are you here? (hopefully not just to sleep) There will be a quiz! Science 14 May 2010: Vol. 328. no. 5980, pp. 876 - 878 DOI: 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