Error Propagation Through a Network With Non-Uniform Failure.

A central concern of network operators is to estimate the probability of anincident that affects a significant part and thus may yield to a breakdown. Weanswer this question by modeling how a failure of either a node or an edge willaffect the rest of the network using percolation theory. Our model is generalin the sense that it only needs two inputs: the topology of the network and thechances of failure of its components. These chances may vary to representdifferent types of edges having different tendencies to fail. We illustrate theapproach by an example, for which we can even obtain closed form expressionsfor the likelihood of an outbreak remaining bounded or spreading unlimitedly.