2004/01/31 by Z. Burda, J. Jurkiewicz, A. Krzywicki · 4 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Computer science #Mathematics #Opinion Dynamics and Social Influence #Statistics #Stochastic processes and statistical mechanics #Uncorrelated #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.70.026106
published as Phys. Rev. E 70, 026106 (2004) · 7 pages, 7 eps figures, 2-column revtex format, references added
openalex publication_date 2004/08/16 · arxiv created 2004/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper is a direct continuation of an earlier work, where we studied Erdös-Rényi random graphs perturbed by an interaction Hamiltonian favoring the formation of short cycles. Here, we generalize these results. We keep the same interaction Hamiltonian but let it act on general graphs with uncorrelated nodes and an arbitrary given degree distribution. It is shown that the results obtained for Erdös-Rényi graphs are generic, at the qualitative level. However, scale-free graphs are an exception to this general rule and exhibit a singular behavior, studied thoroughly in this paper, both analytically and numerically.