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Matching graphs with unique node labels

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Abstract

A special class of graphs is introduced in this paper. The graphs belonging to this class are characterised by the existence of unique node labels. A number of matching algorithms for graphs with unique node labels are developed. It is shown that problems such as graph isomorphism, subgraph isomorphism, maximum common subgraph (MCS) and graph edit distance (GED) have a computational complexity that is only quadratic in the number of nodes. Moreover, computing the median of a set of graphs is only linear in the cardinality of the set. In a series of experiments, it is demonstrated that the proposed algorithms run very fast in practice. The considered class makes the matching of large graphs, consisting of thousands of nodes, computationally tractable. We also discuss an application of the considered class of graphs and related matching algorithms to the classification and detection of abnormal events in computer networks.

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Authors and Affiliations

  1. ISR Division, DSTO, PO Box 1500, Edinburgh, SA, 5111, Australia

    Peter J. Dickinson & Miro Kraetzl

  2. Institut für Informatik und angewandte Mathematik, Universität Bern, Neubrückstrasse 10, CH-3012, Bern, Switzerland

    Horst Bunke

  3. ITR, University of South Australia, Mawson Lakes, SA, 5095, Australia

    Arek Dadej

Authors
  1. Peter J. Dickinson
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  2. Horst Bunke
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  3. Arek Dadej
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  4. Miro Kraetzl
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Correspondence to Horst Bunke.

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Dickinson, P.J., Bunke, H., Dadej, A. et al. Matching graphs with unique node labels. Pattern Anal Applic 7, 243–254 (2004). https://doi.org/10.1007/s10044-004-0222-5

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