The distance backbone of complex networks

TL;DR

This paper introduces a method to identify a minimal distance backbone in weighted networks, capturing essential shortest paths and revealing redundancy that underpins network robustness across various real-world systems.

Contribution

It presents a novel graph reduction technique that preserves all shortest paths and characterizes the triangular geometry of network edges, enhancing understanding of network complexity.

Findings

Distance backbone is very small in large networks

Redundancy is extensive, supporting network robustness

Method applies across diverse domains like air traffic and brain networks

Abstract

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that includes all possible measures of path length for weighted graphs. The result, without breaking the graph into smaller components, is a distance backbone subgraph sufficient to compute all shortest paths. This is important for understanding the dynamics of spread and communication phenomena in real-world networks. The general methodology we formally derive yields a principled graph reduction technique and provides a finer characterization of the triangular geometry of all edges -- those that contribute to shortest paths and those that do not but are involved in other network phenomena. We demonstrate that the distance backbone is very small in large networks across domains ranging from air traffic to the human brain connectome, revealing that network robustness to attacks and failures seems to stem from surprisingly vast amounts of redundancy.