Ihara zeta function for graphs: non-backtracking walks, prime cycles, and spectral analysis via det(I - uB).
"The Ihara zeta function encodes all non-backtracking closed walks - the 'prime cycles' of a graph."
The Ihara zeta function generalizes the Riemann zeta function to graphs:
For a graph G, the Ihara zeta function is:
ζ_G(u) = ∏_{[C]} (1 - u^{|C|})^{-1}