Current redistribution in resistor networks: Fat-tail statistics in regular and small-world networks

J. Lehmann und J. Bernasconi

Phys. Rev. E 95, 032310 (2017)

Preprint: arXiv:1610.06686

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

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