Fluctuation-dissipation relations for complex networks

Abstract

In the paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing susceptibilities of different networks to changes in external fields. In the case of networks with a given degree sequence, we argue that the scale-free topologies of real-world networks may arise as a result of self-organization of real systems into sparse structures with low susceptibility to random external perturbations. We also show that the ensembles of networks with noninteracting links (both uncorrelated and with two-point correlations) are equivalent to random networks with hidden variables.