Ihara zeta function

The Ihara zeta function closely resembles the Selberg zeta function, and is used to relate the spectrum of the adjacency matrix of a graph to its Euler characteristic. It is given by

<math>\zeta_M(t) = \frac{1}{\det (I-tM)}<math>

where M is the adjacency matrix.

The Ihara zeta function plays an important role in the study of free groups, spectral graph theory, and dynamical systems.