Weighted graph characteristics from oriented line graph polynomials

We develop a novel method for extracting graph characteristics from edge-weighted graphs, based on an extension of the Ihara zeta function from unweighted to edge-weighted graphs. This is effected by generalizing the determinant form of the Ihara zeta function. We use the set of the reciprocal polynomial coefficients of the resulting Ihara zeta function, i.e. the Ihara coefficients, to construct our characterization. We also present a spectral analysis of the edge-weighted graph Ihara coefficients and indicate their advantages over graph spectral methods. Experimental results reveal that the Ihara coefficients are effective for the purpose of clustering edge-weighted graphs.