title: Temporal-varying failures of nodes in networks.
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.
authors.affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy.|Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel.
authors.forename: Georgie
authors.initials: G
authors.lastname: Knight
authors.affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy.
authors.forename: Giampaolo
authors.initials: G
authors.lastname: Cristadoro
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Dresden 01187, Germany.
authors.forename: Eduardo G
authors.initials: EG
authors.lastname: Altmann