Link cascades in complex networks: A mean-field approach

Cascade models on networks have been used extensively to study cascade failure in complex systems. However, most current models consider failure caused by node damage and neglect the possibility of link damage, which is relevant to transportation, social dynamics, biology, and medicine. In an attempt to generalize conventional cascade models to link damage, we propose a link cascade model based on the standard independent cascade model, which is then solved via both numerical simulation and analytic approximation. We find that the probability that a node loses all its links due to link damage exhibits a minimum as a function of node degree, indicating that there exists an optimal degree for a node to be most resistant to link damage. We apply our model to investigate the sign distribution in a real-world signed social network and find that such an optimal degree does exist in a real-world dataset.