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Biased random walks on Kleinberg’s spatial networks

Author

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  • Pan, Gui-Jun
  • Niu, Rui-Wu

Abstract

We investigate the problem of the particle or message that travels as a biased random walk toward a target node in Kleinberg’s spatial network which is built from a d-dimensional (d=2) regular lattice improved by adding long-range shortcuts with probability P(rij)∼rij−α, where rij is the lattice distance between sites i and j, and α is a variable exponent. Bias is represented as a probability p of the packet to travel at every hop toward the node which has the smallest Manhattan distance to the target node. We study the mean first passage time (MFPT) for different exponent α and the scaling of the MFPT with the size of the network L. We find that there exists a threshold probability pth≈0.5, for p≥pth the optimal transportation condition is obtained with an optimal transport exponent αop=d, while for 0pth, and increases with L less than a power law and get close to logarithmical law for 0

Suggested Citation

  • Pan, Gui-Jun & Niu, Rui-Wu, 2016. "Biased random walks on Kleinberg’s spatial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 509-515.
    • Handle: RePEc:eee:phsmap:v:463:y:2016:i:c:p:509-515
    DOI: 10.1016/j.physa.2016.07.036
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