Hypergraphs, Characteristic Polynomials and the Ihara Zeta Function

Authors:
Peng Ren;Tatjana Aleksić;Richard C. Wilson;Edwin R. Hancock
Affiliations:
Department of Computer Science, The University of York, York, UK YO10 5DD;Faculty of Science, University of Kragujevac, Kragujevac, Serbia 34000;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:
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
Year:
2009

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Abstract

In this paper we make a characteristic polynomial analysis on hypergraphs for the purpose of clustering. Our starting point is the Ihara zeta function [8] which captures the cycle structure for hypergraphs. The Ihara zeta function for a hypergraph can be expressed in a determinant form as the reciprocal of the characteristic polynomial of the adjacency matrix for a transformed graph representation. Our hypergraph characterization is based on the coefficients of the characteristic polynomial, and can be used to construct feature vectors for hypergraphs. In the experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering hypergraphs.