A New Determinant Expression of the Zeta Function for a Hypergraph

Iwao Sato

Abstract


Recently, Storm defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it by the Perron-Frobenius operator of a digraph and a deformation of the usual Laplacian of a graph. We present a new determinant expression for the Ihara-Selberg zeta function of a hypergraph, and give a linear algebraic proof of Storm's Theorem. Furthermore, we generalize these results to the Bartholdi zeta function of a hypergraph.


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