Pattern vectors from the Ihara zeta function

This paper shows how to construct pattern vectors from the Ihara zeta function for the purposes of characterizing graph structures. To avoid the risk of sampling the meaningless infinities at the poles of the Ihara zeta function, we take use of the coefficients of the polynomial of the reciprocal zeta function. The proposed pattern vector is proved to be permutation invariant to the node order of the associated graph. Its components can be computed from a characteristic polynomial derived from the original graph. We apply the proposed scheme to graph clustering.