Kemeny's constant and the effective graph resistance

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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.

Original languageEnglish
Pages (from-to)231-244
Number of pages14
JournalLinear Algebra and Its Applications
Publication statusPublished - 2017


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

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