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We define a new weighted zeta function for a finite digraph and obtain itsdeterminant expression called the Ihara expression. The graph zeta function isa generalization of the weighted graph zeta function introduced in previousresearch. That is, our result makes it possible to derive the Ihara expressionsof the previous graph zeta functions for any finite digraphs.

The Ihara expression of a generalization of the weighted zeta function on a finite digraph