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# 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.

Last updated: 10-18-2005 05:17:55
03-10-2013 05:06:04