Critical phenomena in networks

TL;DR

This paper develops a phenomenological theory describing how critical phenomena in networks are influenced by the degree distribution, showing deviations from mean-field behavior and aligning with observed network behaviors.

Contribution

The paper introduces a new phenomenological framework that accounts for arbitrary degree distributions, revealing their impact on critical phenomena in networks.

Findings

Critical behavior depends on the degree distribution P(k).

Deviations from mean-field behavior are observed.

Theory aligns with empirical network data.

Abstract

We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly from the standard mean-field behavior. The critical behavior observed in various networks is analyzed and found to be in agreement with the theory.