Kemeny's constant and its relation to the effective graph resistance has been established for regular graphs by Palacios et al. . 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.
- Effective graph resistance or Kirchhoff index
- Kemeny constant
- Moore–Penrose pseudo-inverse
- Multiplicative degree-Kirchhoff index
- Spectral graph theory