Hierarchical structure and the prediction of missing links in networks

TL;DR

This paper introduces a method to infer hierarchical organization in networks, explaining their properties and enabling accurate prediction of missing links, highlighting hierarchy as a key principle in complex network structure.

Contribution

The paper presents a novel technique for inferring hierarchical structures in networks and demonstrates its effectiveness in explaining network properties and predicting missing links.

Findings

Hierarchical structure explains network properties like degree distribution and clustering.

The method accurately predicts missing links in various network types.

Hierarchy serves as a central organizing principle in complex networks.

Abstract

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into groups that further subdivide into groups of groups, and so forth over multiple scales. In many cases these groups are found to correspond to known functional units, such as ecological niches in food webs, modules in biochemical networks (protein interaction networks, metabolic networks, or genetic regulatory networks), or communities in social networks. Here we present a general technique for inferring hierarchical structure from network data and demonstrate that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks, such as right-skewed degree distributions, high clustering coefficients, and short path lengths. We further show that knowledge of hierarchical structure can be used to predict missing connections in partially known networks with high accuracy, and for more general network structures than competing techniques. Taken together, our results suggest that hierarchy is a central organizing principle of complex networks, capable of offering insight into many network phenomena.