Two-Dimensional Centrality of Asymmetric Social Network

  • Akinori OkadaEmail author
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


The purpose of the present study is to introduce a procedure to derive the centrality of an asymmetric social network, where the relationships among actors are asymmetric. The procedure is based on the singular value decomposition of an asymmetric matrix of friendship relationships among actors. Two kinds of the centrality are introduced; one is the centrality of extending friendship relationships from the actor to the other actors, and the other is the centrality of accepting friendship relationships from the other actors to the actor. The present procedure is based on the two largest singular values not only on the largest singular value. Each actor has two sets of the centrality; each consists of the centrality of extending and of the centrality of accepting friendship relationships. An application to help or advice relationships among managers in a company is shown.


  1. Bonacich, P. (1972). Factoring and weighting approaches to clique identification. Journal of Mathematical Sociology, 2, 113–120.CrossRefGoogle Scholar
  2. Bonacich, P. (1991). Simultaneous group and individual centralities. Social Networks, 13, 155–168.CrossRefGoogle Scholar
  3. Bonacich, P., & Lloyd, P. (2001). Eigenvector-like measures of centrality for asymmetric relations. Social Networks, 23, 191–201.CrossRefGoogle Scholar
  4. Borg, I., & Groenen, P. J. K. (2005). Modern multidimensional scaling: Theory and applications (2nd edition). New York: Springer.zbMATHGoogle Scholar
  5. Greenacre, M. (2000). Correspondence analysis of square asymmetric matrices. Applied Statistics, 49, 297–310.zbMATHMathSciNetGoogle Scholar
  6. Krackhardt, D. (1987). Cognitive social structures. Social Networks, 9, 109–134.CrossRefMathSciNetGoogle Scholar
  7. Okada, A. (2008). Two-dimensional centrality of a social network. In C. Preisach, L. Burkhardt, & L. Schmidt-Thieme (Eds.), Data analysis, machiine learning and applications (pp. 381–388). Heidelberg: Springer.CrossRefGoogle Scholar
  8. Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. Cambridge, UK: Cambridge University Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Graduate School of Management and Information SciencesTama UniversityTama-shiJapan

Personalised recommendations