Critical phenomena on heterogeneous small-world networks

TL;DR

This paper investigates critical phenomena on heterogeneous small-world networks with scale-free properties and short-loops, demonstrating the robustness of critical behavior despite network complexity.

Contribution

It derives a self-consistent equation for the order parameter and proves the invariance of critical behavior in complex networks with short-loops.

Findings

Critical behavior is infinitely robust to short-loops.

Derived a self-consistent equation for the order parameter.

Proved invariance of critical phenomena on complex networks.

Abstract

We consider critical phenomena on heterogeneous small-world networks having a scale-free character but also arbitrary short-loops. After deriving the self-consistent equation for the order parameter and the critical surface, we prove that the critical behavior on complex networks is in fact infinitely robust with respect to the presence of arbitrary short-loops.