Predicting the cascading dynamics in complex networks via the bimodal failure size distribution

TL;DR

This paper investigates the bimodal distribution of cascade sizes in complex networks, revealing its ubiquity and proposing a hybrid load metric (HLM) to predict final cascade sizes more accurately than existing methods.

Contribution

The study uncovers the widespread bimodal nature of cascade sizes and introduces the HLM metric for improved prediction of cascade outcomes in complex networks.

Findings

Bimodal distribution is common in synthetic and real networks.

Large cascades result from initial high load failures or multiple cascade rounds.

HLM outperforms traditional centrality metrics in predicting cascade sizes.

Abstract

Cascading failure as a systematic risk occurs in a wide range of real-world networks. Cascade size distribution is a basic and crucial characteristic of systemic cascade behaviors. Recent research works have revealed that the distribution of cascade sizes is a bimodal form indicating the existence of either very small cascades or large ones. In this paper, we aim to understand the properties and formation of such bimodal distribution of cascade sizes in complex networks, and further predict the final cascade size. We first find that the bimodal distribution of cascade sizes is ubiquitous in both synthetic and real networks. Moreover, the large cascade sizes distributed in the right peak of bimodal distribution are resulted from either the failure of nodes with high load at the first step of the cascade or multiple rounds of cascades triggered by the initial failure. Accordingly, we propose a hybrid load metric (HLM), which combines the load of the initial broken node and the load of failed nodes triggered by the initial failure, to predict the final size of cascading failures. Finally, we validate the effectiveness of HLM by computing the accuracy of identifying the cascades belonging to the right and left peaks of the bimodal distribution. The results show that HLM is a better predictor than commonly used network centrality metrics in both synthetic and real-world networks.