Graph isomorphisms and automorphisms via spectral signatures

Dan Raviv, Ron Kimmel, Alfred M. Bruckstein

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number6378375
Pages (from-to)1985-1993
Number of pages9
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume35
Issue number8
DOIs
StatePublished - 2013
Externally publishedYes

Keywords

  • Graph isomorphism
  • graph Laplacian
  • graph automorphisms
  • graph symmetries
  • heat kernel maps
  • heat kernel signatures

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