Mean first passage time and Kemeny's constant using generalized inverses of the combinatorial Laplacian

In the field of random walks, the mean first passage time matrix and the Kemeny's constant allow us to deepen into the study of networks. For a transition matrix P, we can observe in the literature how the authors characterize mean first passage time using generalized inverses of I-P and its as...

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Detalles Bibliográficos
Autores: Carmona Mejías, Ángeles|||0000-0001-7713-1066, Jiménez Jiménez, María José|||0000-0003-3502-462X, Martin Llopis, Álvar|||0000-0002-9542-5524
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/388204
Acceso en línea:https://hdl.handle.net/2117/388204
https://dx.doi.org/10.1080/03081087.2023.2209271
Access Level:acceso abierto
Palabra clave:Random walk
Mean first passage time matrix
Kemeny's constant
Combinatorial Laplacian
Group inverse
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario:In the field of random walks, the mean first passage time matrix and the Kemeny's constant allow us to deepen into the study of networks. For a transition matrix P, we can observe in the literature how the authors characterize mean first passage time using generalized inverses of I-P and its associated group inverse. In this paper, we focus on obtaining expressions for the mentioned parameters in terms of generalized inverses of the combinatorial Laplacian. For that, we first analyse the structure and the relations between any generalized inverse and the group inverse of the combinatorial Laplacian. Then, we get closed-formulas for mean first passage matrix and Kemeny's constant based on the group inverse of the combinatorial Laplacian. As an example, we consider wheel networks.