Temporal-varying failures of nodes in networks

TL;DR

This paper introduces a new measure called failure-centrality to evaluate node importance in networks with time-varying failures, considering loop structures and community effects, with analytical and empirical validation.

Contribution

It develops approximations for failure-centrality in dynamic failure scenarios and explores how external interventions can alter node importance.

Findings

Failure-centrality accounts for loop structures beyond degree.

Long failure cycles cause higher escape rates than stochastic failure models.

Communities cause deviations from hub-based failure predictions.

Abstract

We consider networks in which random walkers are removed because of the failure of specific nodes. We interpret the rate of loss as a measure of the importance of nodes, a notion we denote as failure-centrality. We show that the degree of the node is not sufficient to determine this measure and that, in a first approximation, the shortest loops through the node have to be taken into account. We propose approximations of the failure-centrality which are valid for temporal-varying failures and we dwell on the possibility of externally changing the relative importance of nodes in a given network, by exploiting the interference between the loops of a node and the cycles of the temporal pattern of failures. In the limit of long failure cycles we show analytically that the escape in a node is larger than the one estimated from a stochastic failure with the same failure probability. We test our general formalism in two real-world networks (air-transportation and e-mail users) and show how communities lead to deviations from predictions for failures in hubs.