On the origins of hierarchy in complex networks.

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 nonadaptive 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.