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The redistribution of electrical currents in resistor networks aftersingle-bond failures is analyzed in terms of current-redistribution factorsthat are shown to depend only on the topology of the network and on the valuesof the bond resistances. We investigate the properties of thesecurrent-redistribution factors for regular network topologies (e.g.$d$-dimensional hypercubic lattices) as well as for small-world networks. Inparticular, we find that the statistics of the current redistribution factorsexhibits a fat-tail behavior, which reflects the long-range nature of thecurrent redistribution as determined by Kirchhoff's circuit laws.

Current Redistribution in Resistor Networks: Fat-Tail Statistics in Regular and Small-World Networks