Perturbing General Uncorrelated Networks

Details Perturbing General Uncorrelated Networks Perturbing General Uncorrelated Networks

2004-01-17

arxiv.org/abs/cond-mat/0401310v2

Phys. Rev. E 70, 026106 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 7 eps figures, 2-column revtex format, references added

Scientific paper

10.1103/PhysRevE.70.026106

This paper is a direct continuation of an earlier work, where we studied Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring 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 Erd\"os-R\'enyi graphs are generic, at the qualitative level. However, scale-free graphs are an exception to this general rule and exhibit a singular behaviour, studied thoroughly in this paper, both analytically and numerically.

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