Topologically biased random walk and community finding in networks

Vinko Zlatić, Andrea Gabrielli, and Guido Caldarelli
Phys. Rev. E 82, 066109 – Published 8 December 2010

Abstract

We present an 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 to study the features of random walks vs parameter values. Furthermore, we show an analysis of the spectral gap maximum associated with the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow ad hoc algorithms for the exploration of complex networks and their communities.

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  • Received 17 March 2010

DOI:https://doi.org/10.1103/PhysRevE.82.066109

©2010 American Physical Society

Authors & Affiliations

Vinko Zlatić1,2, Andrea Gabrielli1,3, and Guido Caldarelli1,4,5

  • 1Istituto Sistemi Complessi–CNR, UOS “Sapienza,” Dipartimento di Fisica, Università “Sapienza,” Piazzale A. Moro 2, 00185 Rome, Italy
  • 2Theoretical Physics Division, Rudjer Bošković Institute, P.O. Box 180, HR-10002 Zagreb, Croatia
  • 3Istituto dei Sistemi Complessi–CNR, Via dei Taurini 19, 00185 Rome, Italy
  • 4LINKALAB, Via San Benedetto 88, 09129 Cagliari, Italy
  • 5London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London W1K 2NY, United Kingdom

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Issue

Vol. 82, Iss. 6 — December 2010

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