Journal of Theoretical Probability

, Volume 4, Issue 1, pp 101–109 | Cite as

Random walks and the effective resistance of networks

  • Prasad Tetali


In this article we present an interpretation ofeffective resistance in electrical networks in terms of random walks on underlying graphs. Using this characterization we provide simple and elegant proofs for some known results in random walks and electrical networks. We also interpret the Reciprocity theorem of electrical networks in terms of traversals in random walks. The byproducts are (a) precise version of thetriangle inequality for effective resistances, and (b) an exact formula for the expectedone-way transit time between vertices.

Key Words

Electrical networks electrical impedance random walks Markov chains 


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Prasad Tetali
    • 1
  1. 1.Department of Computer ScienceCourant Institute of Mathematical SciencesNew York

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