Local rewiring rules for evolving complex networks

TL;DR

This paper investigates how local and global link rewiring in directed networks with fixed out-degree influence degree distribution, revealing the emergence of exponential distributions with high-degree outliers.

Contribution

It introduces a model combining growth, global, and local rewiring mechanisms, analyzing their combined effects on network degree distribution.

Findings

Rewiring leads to exponential degree distributions.

High-degree outliers emerge under specific growth conditions.

Local rewiring influences network topology and degree variance.

Abstract

The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global rewiring and local rewiring. During a rewiring phase a node is randomly selected, one of its out-going edges is detached from its destination then re-attached to the network in one of two possible ways; either globally to a randomly selected node, or locally to a descendant of a descendant of the originally selected node. Although the probability of attachment to a node increases with its connectivity, the probability of detachment also increases, the result is an exponential degree distribution with a small number of outlying nodes that have extremely large degree. We explain these outliers by identifying the circumstances for which a set of nodes can grow to very high degree.