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Correlated random networks

Johannes Berg·Michael Lässig
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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 $Z=\sum_{\c} \exp {[}-β\H(\c) {]}$. The simplest cases are uncorrelated random networks such as the well-known Erdös-Rény graphs. Here we study more general interactions $\H(\c)$ which lead to {\em correlations}, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in {\em optimized} networks described by partition functions in the limit $β\to \infty$. They are argued to be a crucial signature of evolutionary design in biological networks.

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BibTeXRIS

Johannes Berg, Michael Lässig. 2002-10-20. Correlated random networks. https://doi.org/10.1103/physrevlett.89.228701

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