Identification of phases in scale-free networks

TL;DR

This paper explores the relationship between phase transitions and power-law distributions in scale-free networks, providing a method to partition networks into high- and low-connectivity regions with applications across various fields.

Contribution

It introduces an unbiased partitioning method for complex networks based on phase transition analysis, applicable to diverse systems like software, finance, and materials.

Findings

Quantifies the link between second-order phase transitions and power-law behavior.

Provides a novel method for network partitioning into connectivity regions.

Demonstrates applications in software architecture, finance, and aerogels.

Abstract

There is a pressing need for a description of complex systems that includes considerations of the underlying network of interactions, for a diverse range of biological, technological and other networks. In this work relationships between second-order phase transitions and the power laws associated with scale-free networks are directly quantified. A unique unbiased partitioning of complex networks (exemplified in this work by software architectures) into high- and low-connectivity regions can be made. Other applications to finance and aerogels are outlined.