Bicomponents and the robustness of networks to failure

TL;DR

This paper investigates the structure and robustness of bicomponents in networks, revealing that most networks have a giant bicomponent that persists under node failures, indicating high resilience.

Contribution

It introduces a combined analytic and numerical approach to study bicomponents in real and model networks, highlighting their size and robustness under failures.

Findings

Most networks have a giant bicomponent coinciding with the giant component.

Real networks generally follow the pattern of having a large, resilient bicomponent.

Networks can remain robust with large bicomponents until nearly all nodes are removed.

Abstract

A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes them to become disconnected. This definition leads us naturally to consider bicomponents, subnetworks in which every node has a robust connection of this kind to every other. Here we study bicomponents in both real and model networks using a combination of exact analytic techniques and numerical methods. We show that standard network models predict there to be essentially no small bicomponents in most networks, but there may be a giant bicomponent, whose presence coincides with the presence of the ordinary giant component, and we find that real networks seem by and large to follow this pattern, although there are some interesting exceptions. We study the size of the giant bicomponent as nodes in the network fail, using a specially developed computer algorithm based on data trees, and find in some cases that our networks are quite robust to failure, with large bicomponents persisting until almost all vertices have been removed.