  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 optimal degree does exist in real-world dataset.
