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We study a cascading edge failure mechanism on a connected random graph witha prescribed degree sequence, sampled using the configuration model. Thismechanism prescribes that every edge failure puts an additional strain on theremaining network, possibly triggering more failures. We show that under acritical loading mechanism that depends on the global structure of the network,the number of edge failure exhibits scale-free behavior (up to a certainthreshold). Our result is a consequence of the failure mechanism and the graphtopology. More specifically, the critical loading mechanism leads to scale-freefailure sizes for any network where no disconnections take place. Thedisintegration of the configuration model ensures that the dominantcontribution to the failure size comes from edge failures in the giantcomponent, for which we show that the scale-free property prevails. We provethis rigorously for sublinear thresholds, and we explain intuitively why theanalysis follows through for linear thresholds. Moreover, our result holds forother graph structures as well, which we validate with simulation experiments.

Failure behavior in a connected configuration model under a critical loading mechanism