Advances in Computational Mathematics

, Volume 39, Issue 2, pp 311–325 | Cite as

An efficient heuristic approach to detecting graph isomorphism based on combinations of highly discriminating invariants

  • Matthias Dehmer
  • Martin Grabner
  • Abbe Mowshowitz
  • Frank Emmert-Streib


The search for an easily computable, finite, complete set of graph invariants remains a challenging research topic. All measures characterizing the topology of a graph that have been developed thus far exhibit some degree of degeneracy, i.e., an inability to distinguish between non-isomorphic graphs. In this paper, we show that certain graph invariants can be useful in substantially reducing the computational complexity of isomorphism testing. Our findings are underpinned by numerical results based on a large scale statistical analysis.


Graph isomorphism Graphs Graph measures Graph topology Uniqueness 

Mathematics Subject Classifications (2010)

05C60 05C75 68R10 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Matthias Dehmer
    • 1
  • Martin Grabner
    • 1
  • Abbe Mowshowitz
    • 2
  • Frank Emmert-Streib
    • 3
  1. 1.Institute for Bioinformatics and Translational ResearchUMITHall in TyrolAustria
  2. 2.Department of Computer ScienceThe City College of New York (CUNY)New YorkUSA
  3. 3.Computational Biology and Machine Learning Lab, Center for Cancer Research and Cell Biology, School of Medicine, Dentistry and Biomedical SciencesQueen’s University BelfastBelfastUK

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