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

:zeta_M(t) = frac{1}{det (I-tM)}

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, especially symbolic dynamics.