Topological phase transition in a network model with preferential attachment and node removal

TL;DR

This paper investigates a generalized network growth model incorporating preferential attachment, random attachment, and node removal, revealing a topological phase transition that shifts the degree distribution from a power law to exponential decay.

Contribution

It introduces a novel model combining multiple attachment mechanisms and node removal, analyzing the resulting phase transition in network topology.

Findings

Identifies a phase transition depending on node removal rate and attachment types.

Shows the degree distribution shifts from power law to exponential tail.

Provides a high-degree expansion method for analyzing complex network dynamics.

Abstract

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we identify a topological phase transition depending on the rate of node removal and the relative strength of preferential vs. random attachment, where the degree distribution goes from a power law to one with an exponential tail.