Correlation of cascade failures and centrality measures in complex networks

Abstract

In complex networks, different nodes have distinct impact on overall functionality and resiliency against failures. Hence, identifying vital nodes is crucial to limit the size of the damage during a cascade failure process, enabling us to identify the most vulnerable nodes and to take solid protection measures to deter them from failure. In this manuscript, we study the correlation between cascade depth, i.e. the number of failed nodes as a consequence of single failure in one of the nodes, and centrality measures including degree, betweenness, closeness, clustering coefficient, local rank, eigenvector centrality, lobby index and information index. Networks behave dissimilarly against cascade failure due to their different structures. Interestingly, we find that node degree is negatively correlated with the cascade depth, meaning that failing a high-degree node has less severe effect than the case when lower-degree nodes fail. Betweenness centrality and local rank show positive correlation with the cascade depth. In order to make networks more resilient against cascade failures, one can remove nodes that ranked high in terms of those centrality measures showing negative correlation with the cascade depth.