English

Scaling in Small-World Resistor Networks

Statistical Mechanics 2007-05-23 v1 Disordered Systems and Neural Networks

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, lαl^{-\alpha}. In this case we find that the average effective system resistance diverges for any non-zero value of α\alpha.

Keywords

Cite

@article{arxiv.cond-mat/0508056,
  title  = {Scaling in Small-World Resistor Networks},
  author = {G. Korniss and M. B. Hastings and K. E. Bassler and M. J. Berryman and B. Kozma and D. Abbott},
  journal= {arXiv preprint arXiv:cond-mat/0508056},
  year   = {2007}
}

Comments

15 pages, 6 figures

R2 v1 2026-07-22T11:20:52.261Z