On Connecting Network Analysis and Cluster Analysis

  • Anuška Ferligoj
  • Vladimir Batagelj
  • Patrick Doreian
Part of the Recent Research in Psychology book series (PSYCHOLOGY)


Actor equivalence is a fundamental concept for the analysis of network representations of social structure. In this paper it is shown that the partitioning of a network in terms of some kind of equivalence (e.g., structural or regular equivalence) is essentially a clustering problem. When searching for the best partition with standard clustering algorithms, a criterion function has to be defined, compatible with the chosen kind of equivalence. Such a criterion function can be constructed indirectly as a function of a compatible (dis)similarity measure between pairs of actors or directly as a function measuring the concordance of a given partition with an ideal partition for the chosen equivalence.


Social Network Criterion Function Cluster Problem Citation Network Indirect Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Batagelj, V. (1991). STRAN — STRucture ANalysis. Manual. Ljubljana: Department of Mathematics, University of Ljubljana.Google Scholar
  2. Batagelj, V., Doreian, P., & Ferligoj, A. (1992). An optimizational approach to regular equivalence. Social Networks, 14, 121–135.CrossRefGoogle Scholar
  3. Batagelj, V., Ferligoj, A., & Doreian, P. (1992). Direct and indirect methods for structural equivalence. Social Networks, 14, 63–90.CrossRefGoogle Scholar
  4. Borgatti, S.P., & Everett, M.G. (1989). The class of all regular equivalences: Algebraic structure and computation. Social Networks, 11, 65–88.CrossRefGoogle Scholar
  5. Burt, R.S. (1976). Positions in networks. Social Forces, 55, 93–122.Google Scholar
  6. Burt, R.S., & Minor, M.J. (1983). Applied network analysis. Beverly Hills: Sage.Google Scholar
  7. Doreian, P. (1988). Equivalence in a social network. Journal of Mathematical Sociology, 13, 243–282.CrossRefGoogle Scholar
  8. Everett, M.G., & Borgatti, S.P. (1988). Calculating role similarities: An algorithm that helps determine the orbits of a graph. Social Networks, 10, 71–91.CrossRefGoogle Scholar
  9. Faust, K. (1988). Comparison of methods for positional analysis: Structural and general equivalences. Social Networks, 10, 313–341.CrossRefGoogle Scholar
  10. Foulds, L.R. (1984). Combinatorial optimization for undergraduates. New York: Springer-Verlag.Google Scholar
  11. Gordon, A.D. (1981). Classification. London: Chapman and Hall.Google Scholar
  12. Hartigan, J.A. (1975). Cluster algorithms. New York: Wiley.Google Scholar
  13. Hummon, N.P., & Carley, K. (1992). Social networks as normal science. Presented at the Annual Sunbelt Social Network Conference, San Diego, February 13–16 1992.Google Scholar
  14. Hummon, N.P., & Doreian, P. (1989). Connectivity in a citation network: The development of dna theory. Social Networks, 11, 39–63.CrossRefGoogle Scholar
  15. Hummon, N.P., & Doreian, P. (1990). Computational methods for social network analysis. Social Networks, 12, 273–288.CrossRefGoogle Scholar
  16. Hummell, H., & Sodeur, W. (1987). Strukturbeschreibung von Positionen in Sozialen Beziehungsnetzen. In F.U. Pappi (Ed.), Methoden der Netzwerk-analyse (pp. 177–202). München: Oldenbourg.Google Scholar
  17. Kuhn, T. (1970). The structure of scientific revolutions. Chicago: Chicago University Press.Google Scholar
  18. Lorrain, F., & White, H.C. (1971). Structural equivalence of individuals in social networks. Journal of Mathematical Sociology, 1, 49–80.CrossRefGoogle Scholar
  19. Pattison, P.E. (1988). Network models; some comments on papers in this special issue. Social Networks, 10, 383–411.CrossRefGoogle Scholar
  20. Sailer, L.D. (1978). Structural equivalence: Meaning and definition, computation and application. Social Networks, 1, 73–90.CrossRefGoogle Scholar
  21. Ward, J.H. (1963). Hierarchical grouping to optimize an objective function. JASA, 58, 236–244.Google Scholar
  22. White, D.R., & Reitz, K.P. (1983). Graph and semigroup homomorphisms on networks of relations. Social Networks, 5, 193–234.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Anuška Ferligoj
    • 1
  • Vladimir Batagelj
    • 2
  • Patrick Doreian
    • 3
  1. 1.Faculty of Social ScienceUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia
  3. 3.Department of SociologyUniversity of PittsburghPittsburghUSA

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