Scaling in small-world resistor networks

2005/08/01 by G. Korniss, M. B. Hastings, Kevin E. Bassler +6
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Complex network #Conductance #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Propagator #Quantum and electron transport phenomena #Quantum mechanics #Resistor #Scaling #Scaling limit #Small-world network #Statistical physics #Statistics #Theoretical and Computational Physics #Value (mathematics) #Zero (linguistics) #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physleta.2005.09.081

published as Physics Letters A 350, 324 (2006) · 15 pages, 6 figures

arxiv created 2005/08/01 · openalex publication_date 2005/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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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