Kemeny's constant and the effective graph resistance

Journal article (2017)

Authors

X. Wang Mathematical Physics -

J.L.A. Dubbeldam Mathematical Physics -

P.F.A. Van Mieghem Network Architectures and Services -

Research Group

Mathematical Physics () (TU Delft)

DOI: https://doi.org/10.1016/j.laa.2017.09.003

Effective graph resistance or Kirchhoff index Kemeny constant Moore–Penrose pseudo-inverse Multiplicative degree-Kirchhoff index Spectral graph theory

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http://resolver.tudelft.nl/uuid:1f46cc50-c3e6-425c-91bb-d05944301420

Published Date

2017

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

Kemeny's constant and its relation to the effective graph resistance has been established for regular graphs by Palacios et al. [1]. Based on the Moore–Penrose pseudo-inverse of the Laplacian matrix, we derive a new closed-form formula and deduce upper and lower bounds for the Kemeny constant. Furthermore, we generalize the relation between the Kemeny constant and the effective graph resistance for a general connected, undirected graph.

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