Issue No. 08 - Aug. (2013 vol. 35)
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
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.
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
A. M. Bruckstein, R. Kimmel and D. Raviv, "Graph Isomorphisms and Automorphisms via Spectral Signatures," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. , pp. 1985-1993, 2013.