Fluctuation-dissipation relations for complex networks

TL;DR

This paper derives fluctuation-dissipation relations for maximum-entropy random networks, linking network susceptibilities to external perturbations, and suggests that real-world scale-free networks may self-organize into low-susceptibility structures.

Contribution

It introduces new fluctuation-dissipation relations for complex networks and connects different network ensembles to hidden-variable models, advancing understanding of network robustness.

Findings

Real-world scale-free networks may self-organize into sparse, low-susceptibility structures.

Ensembles with noninteracting links are equivalent to hidden-variable models.

Derived fluctuation-dissipation relations characterize network responses to external changes.

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.