  On a finite regular graph, (co)resonant states are eigendistributions of the
transfer operator associated to the shift on one-sided infinite
non-backtracking paths. We introduce two pairings of resonant and coresonant
states, the vertex pairing which involves only the dependence on the
initial/terminal vertex of the path, and the geodesic pairing which is given by
integrating over all geodesics the evaluation of the coresonant state on the
first half of the geodesic times the resonant state on the second half. The
main result is that these two pairings coincide up to a constant which depends
on the resonance, i.e. the corresponding eigenvalue of the transfer operator.
