title: Graph isomorphisms and automorphisms via spectral signatures.
abstract: An isomorphism between two graphs is a connectivity preserving bijective mapping between their sets of vertices. Finding isomorphisms between graphs, or between a graph and itself (automorphisms), is of great importance in applied sciences. The inherent computational complexity of this problem is as yet unknown. Here, we introduce an efficient method to compute such mappings using heat kernels associated with the graph Laplacian. While the problem is combinatorial in nature, in practice we experience polynomial runtime in the number of vertices. As we demonstrate, the proposed method can handle a variety of graphs and is competitive with state-of-the-art packages on various important examples.
authors.affiliation: Department of Computer Science, Technion-Israel Institute of Technology, Taub Building, Haifa 32000, Israel. darav@cs.technion.ac.il
authors.forename: Dan
authors.initials: D
authors.lastname: Raviv
authors.forename: Ron
authors.initials: R
authors.lastname: Kimmel
authors.forename: Alfred M
authors.initials: AM
authors.lastname: Bruckstein