Analysis of weighted networks

M. E. J. Newman
Phys. Rev. E 70, 056131 – Published 24 November 2004

Abstract

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum-flow–minimum-cut theorem.

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  • Received 26 July 2004

DOI:https://doi.org/10.1103/PhysRevE.70.056131

©2004 American Physical Society

Authors & Affiliations

M. E. J. Newman

  • Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109-1120, USA and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

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Issue

Vol. 70, Iss. 5 — November 2004

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