Draft:Graph difference


Graph difference or Structural difference is defined as a measure of the number of modifications required to transform an input graph into another.[1] Graph difference is not unique and depends upon the distance measure used. Distance Measures proposed for computing graph difference include Gernet distance[2], Graph edit distance[3], and Wasserstein distance[4].

Problem of computing graph difference is equivalent to computing the Maximum Common Subgraph and is NP-Complete.[5]

  1. ^ Shapiro, Linda G.; Haralick, Robert M. (1981). "Structural Descriptions and Inexact Matching". IEEE Transactions on Pattern Analysis and Machine Intelligence. PAMI-3 (5): 504–519. doi:10.1109/TPAMI.1981.4767144. ISSN 0162-8828. PMID 21868971.
  2. ^ Gernet, Dieter (1979). "Measuring the similarity of complex structures by means of graph grammars". Bulletin of the European Association of Theoretical Computer Science (EATCS) (7): 3–9.
  3. ^ Sanfeliu, Alberto; Fu, King-Sun (1983). "A distance measure between attributed relational graphs for pattern recognition". IEEE Transactions on Systems, Man, and Cybernetics. SMC-13 (3): 353–362. doi:10.1109/TSMC.1983.6313167. ISSN 0018-9472.
  4. ^ Han, Yuehui; Hui, Le; Jiang, Haobo; Qian, Jianjun; Xie, Jin (2022). "Generative Subgraph Contrast for Self-Supervised Graph Representation Learning". In Avidan, Shai; Brostow, Gabriel; Cissé, Moustapha; Farinella, Giovanni Maria; Hassner, Tal (eds.). Computer Vision – ECCV 2022. Lecture Notes in Computer Science. Vol. 13690. Cham: Springer Nature Switzerland. pp. 91–107. doi:10.1007/978-3-031-20056-4_6. ISBN 978-3-031-20056-4.
  5. ^ Bunke, H. (1997-08-01). "On a relation between graph edit distance and maximum common subgraph". Pattern Recognition Letters. 18 (8): 689–694. Bibcode:1997PaReL..18..689B. doi:10.1016/S0167-8655(97)00060-3. ISSN 0167-8655.