The Problem of Action at a Distance in Networks and the Emergence of Preferential Attachment from Triadic Closure

TL;DR

This paper argues that preferential attachment in networks is an emergent phenomenon resulting from local triangle closing mechanisms, supported by a simplified model and experiments on synthetic graphs.

Contribution

It demonstrates that preferential attachment can be derived from local triangle closing, challenging the view of it as an action at a distance mechanism.

Findings

Preferential attachment emerges from triangle closing in network growth.

A simplified model mathematically derives preferential attachment from local mechanisms.

Experiments on synthetic graphs confirm the emergence of preferential attachment from triangle closing.

Abstract

In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of triangles. After a review of the concepts of triangle closing and preferential attachment, we present our argument, as well as a simplified model in which preferential attachment can be derived mathematically from triangle closing. Additionally, we perform experiments on synthetic graphs to demonstrate the emergence of preferential attachment in graph growth models based only on triangle closing.