Pattern Analysis and Applications

, Volume 7, Issue 3, pp 243–254 | Cite as

Matching graphs with unique node labels

  • Peter J. Dickinson
  • Horst BunkeEmail author
  • Arek Dadej
  • Miro Kraetzl
Theoretical Advances


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.


Graph matching Graph isomorphism Maximum common subgraph Graph edit distance Median graph Unique node label 


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Copyright information

© Springer-Verlag London Limited 2004

Authors and Affiliations

  • Peter J. Dickinson
    • 1
  • Horst Bunke
    • 2
    Email author
  • Arek Dadej
    • 3
  • Miro Kraetzl
    • 1
  1. 1.ISR DivisionDSTOEdinburghAustralia
  2. 2.Institut für Informatik und angewandte MathematikUniversität BernBernSwitzerland
  3. 3.ITRUniversity of South AustraliaMawson LakesAustralia

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