A Physics Perspective on the Resistance Distance for Graphs

Mikhail A. Kagan, Brian Mata

Research output: Contribution to journalArticle

Abstract

The notion of resistance distance as a convenient metric for graphs was introduced in Klein (J Math Chem 12:81–95, 1993). It is inspired by the concept of equivalent resistance for electrical circuits and has numerous applications, in particular, in organic chemistry, physics and random walks on graphs. Besides, computing resistance distance of various circuits has always been of interest for electrical engineers. In this paper, we provide a brief review of the concept and a physics perspective on resistance distance, highlighting some useful analytical methods for computing it. To some extend, these methods generalize and build on top of the results presented in Bapat (Math Stud 68(1–4):87–98, 1999, Indian J Pure Appl Math 41(1):1–13, 2010) and Kagan (Am J Phys 83:53–63, 2015). We then illustrate these methods using graphs with rotational symmetry as an example. The same analysis can be applied to computations of the complex impedance of AC-circuits of the same circular topology and can be used to investigate resonance phenomena therein. At the end, we discuss the concept of resistance distance in the context of the Weisfeiler–Leman stabilization.

Original languageEnglish (US)
Pages (from-to)105-115
Number of pages11
JournalMathematics in Computer Science
Volume13
Issue number1-2
DOIs
StatePublished - Jun 1 2019

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Physics
Networks (circuits)
Graph in graph theory
Stabilization
Electrical Circuits
Topology
Rotational symmetry
Computing
Engineers
Analytical Methods
Impedance
Chemistry
Random walk
Resistance
Metric
Generalise
Concepts
Organic Chemistry

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

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A Physics Perspective on the Resistance Distance for Graphs. / Kagan, Mikhail A.; Mata, Brian.

In: Mathematics in Computer Science, Vol. 13, No. 1-2, 01.06.2019, p. 105-115.

Research output: Contribution to journalArticle

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