Topological phase transition in complex networks

TL;DR

This paper investigates how generalized preferential attachment models in complex networks can experience a topological phase transition, shifting from power-law to exponential degree distributions, linked to the breakdown of continuous network dynamics.

Contribution

It introduces the concept of a topological phase transition in generalized preferential attachment networks, expanding understanding of network degree distribution behaviors.

Findings

Networks exhibit a phase transition from power-law to exponential degree distribution.

The transition is associated with the breakdown of continuous variable descriptions.

Generalizations include node removal and edge rewiring.

Abstract

Preferential attachment is a central paradigm in the theory of complex networks. In this contribution we consider various generalizations of preferential attachment including for example node removal and edge rewiring. We demonstrate that generalized preferential attachment networks can undergo a topological phase transition. This transition separates networks having a power-law tail degree distribution from those with an exponential tail. The appearance of the phase transition is closely related to the breakdown of the continuous variable description of the network dynamics.