CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2013 vol.35 Issue No.08 - Aug.

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Issue No.08 - Aug. (2013 vol.35)

pp: 1985-1993

Dan Raviv , Technion, Israel Institute of Technology, Haifa

Ron Kimmel , Technion, Israel Institute of Technology, Haifa

Alfred M. Bruckstein , Technion, Israel Institute of Technology, Haifa

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.

INDEX TERMS

Laplace equations, Heating, Eigenvalues and eigenfunctions, Kernel, Shape, Complexity theory, Equations, heat kernel signatures, Graph isomorphism, graph symmetries, graph automorphisms, graph Laplacian, heat kernel maps

CITATION

Dan Raviv, Ron Kimmel, Alfred M. Bruckstein, "Graph Isomorphisms and Automorphisms via Spectral Signatures",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.35, no. 8, pp. 1985-1993, Aug. 2013, doi:10.1109/TPAMI.2012.260REFERENCES