Threshold for the Outbreak of Cascading Failures in Degree-degree Uncorrelated Networks

TL;DR

This paper derives a theoretical threshold for large-scale cascading failures in degree-degree uncorrelated networks, providing insights to improve network robustness under capacity constraints.

Contribution

It introduces a cascade overload failure model with local load sharing and derives the failure threshold analytically for uncorrelated networks.

Findings

The threshold accurately predicts cascade onset in simulations.

The model helps in designing more robust networks.

The approach applies to networks with limited capacity resources.

Abstract

In complex networks, the failure of one or very few nodes may cause cascading failures. When this dynamical process stops in steady state, the size of the giant component formed by remaining un-failed nodes can be used to measure the severity of cascading failures, which is critically important for estimating the robustness of networks. In this paper, we provide a cascade of overload failure model with local load sharing mechanism, and then explore the threshold of node capacity when the large-scale cascading failures happen and un-failed nodes in steady state cannot connect to each other to form a large connected sub-network. We get the theoretical derivation of this threshold in degree-degree uncorrelated networks, and validate the effectiveness of this method in simulation. This threshold provide us a guidance to improve the network robustness under the premise of limited capacity resource when creating a network and assigning load. Therefore, this threshold is useful and important to analyze the robustness of networks.