Origins of fractality in the growth of complex networks

TL;DR

This paper explores the origins of fractality in complex networks, proposing that hub repulsion leads to self-similar structures, which are essential for functional modularity in biological and other systems.

Contribution

It introduces a renormalization-based framework linking hub disassortativity to fractal network growth, highlighting its role in functional modularity.

Findings

Fractal networks emerge from hub repulsion across scales.

Dispersed hubs are key to self-similarity in networks.

Functional modules like cellular networks require fractal topology.

Abstract

Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective 'repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.