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

TL;DR

This paper introduces a new weighted zeta function for finite digraphs, providing a determinant-based Ihara expression that generalizes previous graph zeta functions and enables broader applications.

Contribution

The paper presents a novel weighted zeta function and derives its Ihara expression, extending the framework to all finite digraphs and unifying previous zeta function formulations.

Findings

Derived the Ihara expression for the new weighted zeta function

Unified previous graph zeta functions within a general framework

Enabled computation of zeta functions for any finite digraph

Abstract

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