Correlated Random Networks

Johannes Berg and Michael Lässig
Phys. Rev. Lett. 89, 228701 – Published 11 November 2002

Abstract

We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix c, and the relevant statistical ensembles are defined in terms of a partition function Z=cexp[βH(c)]. The simplest cases are uncorrelated random networks such as the well-known Erdös-Rényi graphs. Here we study more general interactions H(c) which lead to correlations, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in optimized networks described by partition functions in the limit β. They are argued to be a crucial signature of evolutionary design in biological networks.

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  • Received 16 May 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.228701

©2002 American Physical Society

Authors & Affiliations

Johannes Berg and Michael Lässig

  • Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany

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Issue

Vol. 89, Iss. 22 — 25 November 2002

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