Context Graphs — Representing Formal Concepts by Connected Subgraphs

  • Jens Kötters
  • Heinz Schmidt
  • David McG. Squire
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5548)


The article introduces a representation of a formal context by an undirected graph called a context graph with the formal objects being the nodes of the graph. We use as a defining property for this graph that it contains every concept extent as a connected subgraph. The graph is not uniquely defined by this property — we focus on those graphs that are edge-minimal and present a result with respect to the number of their edges. We then study how the structure of an edge-minimal context graph can be updated to adjust to the subsequent addition of an object to the context. This leads to an incremental construction algorithm that does not require the explicit computation of formal concepts.


Context Graphs Formal Concept Analysis Graph Theory Information Retrieval Navigation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ganter, B., Wille, R.: Formal concept analysis: mathematical foundations. Springer, Berlin (1999)CrossRefMATHGoogle Scholar
  2. 2.
    Wille, R.: Concept lattices and conceptual knowledge systems. Computers and Mathematics with Applications 23(6–9), 493–515 (1992)CrossRefMATHGoogle Scholar
  3. 3.
    Davis, A., Gardner, B.B., Gardner, M.R.: Deep South. Univ. Chicago Press, Chicago (1941)Google Scholar
  4. 4.
    Kuznetsov, S.O., Obiedkov, S.A.: Comparing performance of algorithms for generating concept lattices. Journal of Experimental and Theoretical Artificial Intelligence 14, 189–216 (2002)CrossRefMATHGoogle Scholar
  5. 5.
    Priss, U.: Lattice-based information retrieval. Knowledge Organization 27(3), 132–142 (2000)Google Scholar
  6. 6.
    Carpineto, C.: Conceptual structures in modern information retrieval. In: [16], p. 1Google Scholar
  7. 7.
    Delteil, A., Faron, C., Dieng, R.: Building concept lattices by learning concepts from RDF graphs annotating web documents. In: [16], pp. 191–204Google Scholar
  8. 8.
    Duquenne, V., Chabert, C., Cherfouh, A., Delabar, J.M., Doyen, A.L., Pickering, D.: Structuration of phenotypes/genotypes through Galois lattices and implications. In: The 2001 International Workshop on Concept Lattice-based theory, methods and tools for Knowledge Discovery in Databases, Stanford University, CA, USA, July 30 (2001)Google Scholar
  9. 9.
    Godin, R., Mili, H.: Building and maintaining analysis-level class hierarchies using Galois lattices. In: Paepcke, A. (ed.) The Conference on Object-oriented Programming Systems, Languages and Applications, Washington, DC, pp. 394–410 (1993)Google Scholar
  10. 10.
    Carpineto, C., Romano, G.: Information retrieval through hybrid navigation of lattice representations. International Journal of Human-Computer Studies 45(5), 553–578 (1996)CrossRefGoogle Scholar
  11. 11.
    ter Hofstede, A.H.M., Proper, H.A., van der Weide, T.P.: Query formulation as an information retrieval problem. The Computer Journal 39(4), 255–274 (1996)CrossRefGoogle Scholar
  12. 12.
    Ferré, S.: CAMELIS: Organizing and browsing a personal photo collection with a logical information system. In: Diatta, J., Eklund, P., Liquière, M. (eds.) The International Conference on Concept Lattices and Their Applications. CEUR Workshop Proceedings, vol. 331, pp. 112–123 (2007)Google Scholar
  13. 13.
    Lindig, C.: Fast concept analysis. In: Working with Conceptual Structures - Contributions to ICCS 2000, pp. 152–161. Shaker Verlag (2000)Google Scholar
  14. 14.
    Breiger, R.L.: The duality of persons and groups. In: Wellman, B., Berkowitz, S.D. (eds.) Social Structures: A Network Approach, pp. 83–98. Cambridge University Press, Cambridge (1988)Google Scholar
  15. 15.
    Sowa, J.F.: Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley, Reading (1984)MATHGoogle Scholar
  16. 16.
    Priss, U., Corbett, D.R., Angelova, G. (eds.): ICCS 2002. LNCS, vol. 2393. Springer, Heidelberg (2002)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jens Kötters
    • 1
  • Heinz Schmidt
    • 2
  • David McG. Squire
    • 1
  1. 1.Monash UniversityMelbourneAustralia
  2. 2.RMIT UniversityMelbourneAustralia

Personalised recommendations