Kemeny's constant and the effective graph resistance
X Wang (TU Delft - Mathematical Physics)
Johan Dubbeldam (TU Delft - Mathematical Physics)
Piet van Mieghem (TU Delft - Network Architectures and Services)
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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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