Hypergraph isomorphism using association hypergraphs

Abstract

Association graphs represent a classical tool to deal with the graph matching problem and recently the idea has been generalized to the case of hypergraphs. In this article, the potential of this approach is explored. The proposed framework uses a class of dynamical systems derived from the Baum-Eagon inequality in order to find the maximum (maximal) clique in the association hypergraph, that corresponds to the maximum (maximal) isomorphism between the hypergraphs to be matched. The proposed approach has extensively been tested with experiments on a large synthetic dataset, including hypergraphs of different cardinalities, order and connectivities. In particular the isomorphism version of the problem has been analyzed. The results obtained are impressive in terms of correctness, thus showing that, despite its simplicity, the Baum-Eagon dynamics has an outstanding capacity of finding globally optimal solutions and solving the hypergraph isomorphism problem.