Scaling in Small-World Resistor Networks
G. Korniss, M. B. Hastings, K. E. Bassler, M. J. Berryman, B. Kozma, D. Abbott
Abstract
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point resistance in the large system-size limit. We find that the small-world structure suppresses large network resistances: both the average resistance and its standard deviation approaches a finite value in the large system-size limit for any non-zero density of random links. We also consider a scenario where the link conductance decays as a power of the length of the random links, l-α. In this case we find that the average effective system resistance diverges for any non-zero value of α.
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