Sublinear but Never Superlinear Preferential Attachment by Local Network Growth

TL;DR

This paper explores how local network growth rules based on redirection can produce sublinear preferential attachment, but not superlinear, highlighting limitations of local algorithms in network evolution.

Contribution

It introduces a decaying redirection probability that results in sublinear growth and proves that superlinear growth cannot be achieved with local redirection algorithms.

Findings

Redirection probability decaying with parent degree yields sublinear attachment.

Local redirection algorithms cannot produce superlinear preferential attachment.

The study clarifies limitations of local rules in network growth models.

Abstract

We investigate a class of network growth rules that are based on a redirection algorithm wherein new nodes are added to a network by linking to a randomly chosen target node with some probability 1-r or linking to the parent node of the target node with probability r. For fixed 0<r<1, the redirection algorithm is equivalent to linear preferential attachment. We show that when r is a decaying function of the degree of the parent of the initial target, the redirection algorithm produces sublinear preferential attachment network growth. We also argue that no local redirection algorithm can produce superlinear preferential attachment.