Journal Club Physical Review E

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Presentation transcript:

Journal Club Physical Review E Merril Gersten August 30, 2010

Dynamics of overlapping structures in modular networks Almendral, JA: Physical Review E 82:016115 (2010) Questions addressed: How to find nodes which overlap 2 or more communities (partitions) in a complex graph. Methods: “Dynamical overlapping” in which nodes are treated as oscillators and the instantaneous frequency of an overlapping node (“synchronization interface”) oscillates between the frequencies of its associated modules. Results/Discussion: Method identifies nodes in three real-world networks that serve as bridges between two communities. Computational (experimental) results support an analytical analysis. The quantity kiout/ki can be used to identify overlapping nodes in a graph. Interest to Lab: Work here on edge betweenness partitioning has not addressed the overlap issue.

Previous work: Li, D. Physical Review Letters 101:168701 (2008) G = graph of N coupled Kuramoto oscillators fi = phases of oscillators ki=ith oscillator d = coupling strength aij = elements of adjacency matrix of G [1 (or 0) if link does (doesn’t) exist] wi = frequency of oscillator Ci = overlapping index

G = graph of N coupled Kuramoto oscillators fi = phases of oscillators ki=ith oscillator d = coupling strength aij = elements of adjacency matrix of G [1 (or 0) if link does (doesn’t) exist] wi = frequency of oscillator Ci = overlapping index Mi =module

* * Analytical Results Solution: or Solution: or = in-degree = out-of-module links in depends on bi’s, distribution unknown *