Abstract
After defining the " geodesic flow " on a regular graph, we describe the temporal correlations of two observables. The exponential decay of the correlations is explicitly expressed using the spectral decomposition of the Laplacian. This is a simple and explicit special case of what David Ruelle has called " development in resonant states " for a chaotic dynamical system. This correspondence between eigenfunctions of the Laplacian and resonant states of the geodesic flow also demonstrates the " trace formula ", and the Ihara-Bass formula.
