Perturbing general uncorrelated networks

This paper is a direct continuation of an earlier work, where we studied Erdos-Renyi 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 Erdos-Renyi 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.