Bridges in Complex Networks

TL;DR

This paper investigates the prevalence and importance of bridges in complex networks, introduces a new measure called bridgeness, and provides analytical tools to understand their role in network robustness.

Contribution

It introduces the bridgeness measure and offers an analytical framework for assessing bridge properties in uncorrelated random networks.

Findings

Real networks have more bridges than randomized counterparts.

Certain networks exhibit high bridgeness variance, indicating critical bridges.

Analytical formulas for bridge fraction and bridgeness statistics are provided.

Abstract

A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that real networks typically have more bridges than their completely randomized counterparts, but very similar fraction of bridges as their degree-preserving randomizations. We define a new edge centrality measure, called bridgeness, to quantify the importance of a bridge in damaging a network. We find that certain real networks have very large average and variance of bridgeness compared to their degree-preserving randomizations and other real networks. Finally, we offer an analytical framework to calculate the bridge fraction , the average and variance of bridgeness for uncorrelated random networks with arbitrary degree distributions.