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

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Abstract

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.

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Authors and Affiliations

  1. Institute for Bioinformatics and Translational Research, UMIT, Eduard Wallnoefer Zentrum 1, 6060, Hall in Tyrol, Austria

    Matthias Dehmer & Martin Grabner

  2. Department of Computer Science, The City College of New York (CUNY), 138th Street at Convent Avenue, New York, NY, 10031, USA

    Abbe Mowshowitz

  3. Computational Biology and Machine Learning Lab, Center for Cancer Research and Cell Biology, School of Medicine, Dentistry and Biomedical Sciences, Queen’s University Belfast, 97 Lisburn Road, Belfast, BT9 7BL, UK

    Frank Emmert-Streib

Authors
  1. Matthias Dehmer
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  2. Martin Grabner
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  3. Abbe Mowshowitz
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  4. Frank Emmert-Streib
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Corresponding author

Correspondence to Matthias Dehmer.

Additional information

Research was sponsored by the U.S. Army Research Laboratory and the U.K Ministry of Defense and was accomplished under Agreement Number W911NF-06-3-0001. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S Army Research Laboratory, the U.S. Government, the U.K. Ministry of Defense or the U.K Government. The U.S. and U.K. Governments are authorized to reproduce and distribute for Government purposes notwithstanding any copyright notation hereon. Matthias Dehmer and Martin Grabner thanks the Austrian Science Funds for supporting this work (project P22029-N13). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Dehmer, M., Grabner, M., Mowshowitz, A. et al. An efficient heuristic approach to detecting graph isomorphism based on combinations of highly discriminating invariants. Adv Comput Math 39, 311–325 (2013). https://doi.org/10.1007/s10444-012-9281-0

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  • DOI: https://doi.org/10.1007/s10444-012-9281-0

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