Anomalous scaling in redirection networks

TL;DR

This paper investigates the properties of networks grown through isotropic redirection, revealing leaf proliferation and algebraic degree distributions, and introduces models with similar behavior but more local growth rules.

Contribution

The authors develop a class of models with redirection to leaves that replicate IR network phenomena while maintaining local growth rules, enabling analytical understanding.

Findings

Networks show sublinear leaf scaling as N^μ.

Degree distribution has an algebraic tail with exponent 1+μ.

Models with redirection to leaves mimic IR network properties.

Abstract

In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the number of nonleaves scales sublinearly as $N^\mu$ and the degree distribution has an algebraic tail with exponent $1+\mu$. To understand these mysterious properties, we introduce a class of models with redirection to leaves whenever possible. The resulting networks exhibit qualitatively similar phenomenology to IR networks, but avoid the inherent non-locality of the IR growth rule. These networks admit an analytical description of the leaf degree distribution, from which we extract the exponent $\mu$.