On the Origins of Hierarchy in Complex Networks

TL;DR

This paper introduces a formal framework to analyze the origins and structures of hierarchy in complex networks, revealing distinct groups influenced by random processes and functional constraints.

Contribution

It develops a 3D morphospace of hierarchies, enabling comparison across diverse network types and identifying the underlying factors shaping their organization.

Findings

Four major hierarchical groups identified in the morphospace.

Random networks cluster in two groups, indicating non-adaptive origins.

Ecological and gene networks form two groups driven by functional constraints.

Abstract

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological and social networks. Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified. Two of them match the expected from random networks with similar connectivity, thus suggesting that non-adaptive factors are at work. Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints. These results are consistent with an exploration of the morphospace using in silico evolved networks.