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.
Original language | English |
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Pages (from-to) | 231-244 |
Number of pages | 14 |
Journal | Linear Algebra and Its Applications |
Volume | 535 |
DOIs | |
Publication status | Published - 2017 |
Bibliographical note
Accepted Author ManuscriptKeywords
- Effective graph resistance or Kirchhoff index
- Kemeny constant
- Moore–Penrose pseudo-inverse
- Multiplicative degree-Kirchhoff index
- Spectral graph theory