Scaling in Small-World Resistor 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, $l^{-\alpha }$. In this case we find that the average effective system resistance diverges for any non-zero value of $\alpha$.

15 pages, 6 figures

References in corpus (35)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Finding and evaluating community structure in networks
• Error and attack tolerance of complex networks
• The architecture of complex weighted networks
• Evolution of networks
• Who is the best connected scientist? A study of scientific coauthorship networks
• Resilience of the Internet to random breakdowns
• Synchronization in small-world systems
• Breakdown of the Internet under intentional attack
• Renormalization group analysis of the small-world network model
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Finding Communities in Linear Time: A Physics Approach
• Theory of resistor networks: The two-point resistance
• Application of the lattice Green's function for calculating the resistance of an infinite networks of resistors
• Fluctuations in network dynamics
• Diffusion, localization and dispersion relations on ``small-world'' lattices
• Ising model in small-world networks
• Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations
• Competition in Social Networks: Emergence of a Scale-free Leadership Structure and Collective Efficiency
• XY model in small-world networks
• Small-World Networks: Links with long-tailed distributions
• Anomalous Transport in Complex Networks
• Comment on "Ising model on a small world network"
• Effect of congestion costs on shortest paths through complex networks
• Mean-Field and Anomalous Behavior on a Small-World Network
• Diffusion Processes on Power-Law Small-World Networks
• Testing the Collective Properties of Small-World Networks through Roughness Scaling
• Phase transition in the Ising model on a small-world network with distance-dependent interactions
• Critical Properties of an Ising Model with Dilute Long-range Interactions
• An $\epsilon$-expansion for Small-World Networks
• Virtual Time Horizon Control via Communication Network Design
• Tolerance and Sensitivity in the Fuse Network

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