Topologically biased random walk with application for community finding in networks

Details Topologically biased random walk with application for community finding in networks Topologically biased random walk with application for community finding in networks

2010-03-09

arxiv.org/abs/1003.1883v2

Phys. Rev. E 82, 066109 (2010)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 7 figures

Scientific paper

10.1103/PhysRevE.82.066109

We present a new approach of topology biased random walks for undirected networks. We focus on a one parameter family of biases and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion (PEM) to study the features of random walks {\em vs.} parameter values. Furthermore, we show an analysis of the spectral gap maximum associated to the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow {\em ad hoc} algorithms for the exploration of complex networks and their communities.

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