Graph Characteristics from the Ihara Zeta Function

Authors:
Peng Ren;Richard C. Wilson;Edwin R. Hancock
Affiliations:
Department of Computer Science, The University of York, York, UK YO10 5DD;Department of Computer Science, The University of York, York, UK YO10 5DD;Department of Computer Science, The University of York, York, UK YO10 5DD
Venue:
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Year:
2008

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Abstract

This paper shows how to extract permutation invariant graph characteristics from the Ihara zeta function. In a previous paper, we have shown that the Ihara zeta function leads to a polynomial characterization of graph structure, and we have shown empirically that the coefficients of the polynomial can be used as to cluster graphs. The aim in this paper is to take this study further by showing how to select the most significant coefficients and how these can be used to gauge graph similarity. Experiments on real-world datasets reveal that the selected coefficients give results that are significantly better than those obtained with the Laplacian spectrum.