Universal self-similarity of hierarchical communities formed through a general self-organizing principle

TL;DR

This paper uncovers universal scaling laws governing self-similar hierarchical community structures across diverse real-world networks, supported by a phenomenological model based on node similarity and property differences.

Contribution

It identifies universal scaling laws and proposes a general self-organizing principle consistent with Hakens principle for hierarchical community formation.

Findings

Universal scaling laws in biological, infrastructural, and social networks

A phenomenological model replicates observed scaling relations

Self-organization minimizes property differences within communities

Abstract

Emergence of self-similarity in hierarchical community structures is ubiquitous in complex systems. Yet, there is a dearth of universal quantification and general principles describing the formation of such structures. Here, we discover universality in scaling laws describing self-similar hierarchical community structure in multiple real-world networks including biological, infrastructural, and social networks. We replicate these scaling relations using a phenomenological model, where nodes with higher similarity in their properties have greater probability of forming a connection. A large difference in their properties forces two nodes into different communities. Smaller communities are formed owing to further differences in node properties within a larger community. We discover that the general self-organizing principle is in agreement with Hakens principle; nodes self-organize into groups such that the diversity or differences between properties of nodes in the same community is minimized at each scale and the organizational entropy decreases with increasing complexity of the organized structure.