The Hierarchical Backbone of Complex Networks

TL;DR

This paper introduces a method to extract and analyze the hierarchical backbone of complex directed networks using transition matrices, revealing their hierarchical structure through new metrics like hierarchical degree and successors.

Contribution

It presents a novel approach to identify and characterize the hierarchical backbone of directed networks based on transition matrix interpretation.

Findings

Effective extraction of hierarchical backbone from real-world networks

Introduction of hierarchical degree and successors as new metrics

Application to word associations and gene sequencing data

Abstract

Given any complex directed network, a set of acyclic subgraphs - the hierarchical backbone of the network - can be extracted that will provide valuable information about its hierarchical structure. The current paper presents how the interpretation of the network weight matrix as a transition matrix allows the hierarchical backbone to be identified and characterized in terms of the concepts of hierarchical degree, which expresses the total number of virtual edges established along successive transitions, and of hierarchical successors, namely the number of nodes accessible from a specific node while moving successive hierarchical levels. The potential of the proposed approach is illustrated with respect to word associations and gene sequencing data.