Displaying similar documents to “Markov product of positive definite kernels and applications to Q-matrices of graph products”

Tridiagonal matrices and spectral properties of some graph classes

Milica Andelić, Zhibin Du, Carlos M. da Fonseca, Slobodan K. Simić (2020)

Czechoslovak Mathematical Journal

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A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula for the characteristic polynomial of any chain graph and we show that it can be expressed using the determinant of a particular tridiagonal matrix. Then this fact is applied to show that in a certain interval a chain graph does not have any nonzero eigenvalue. A similar result is provided for threshold...

Graph fibrations, graph isomorphism, and PageRank

Paolo Boldi, Violetta Lonati, Massimo Santini, Sebastiano Vigna (2006)

RAIRO - Theoretical Informatics and Applications

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PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and , a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the values that PageRank...