Small Worlds Among Interlocking Directors: Network Structure and Distance in Bipartite Graphs

  • Garry Robins
  • Malcolm Alexander


We describe a methodology to examine bipartite relational data structures as exemplified in networks of corporate interlocking. These structures can be represented as bipartite graphs of directors and companies, but direct comparison of empirical datasets is often problematic because graphs have different numbers of nodes and different densities. We compare empirical bipartite graphs to simulated random graph distributions conditional on constraints implicit in the observed datasets. We examine bipartite graphs directly, rather than simply converting them to two 1-mode graphs, allowing investigation of bipartite statistics important to connection redundancy and bipartite connectivity. We introduce a new bipartite clustering coefficient that measures tendencies for localized bipartite cycles. This coefficient can be interpreted as an indicator of inter-company and inter-director closeness; but high levels of bipartite clustering have a cost for long range connectivity. We also investigate degree distributions, path lengths, and counts of localized subgraphs. Using this new approach, we compare global structural properties of US and Australian interlocking company directors. By comparing observed statistics against those from the simulations, we assess how the observed graphs are structured, and make comparisons between them relative to the simulated graph distributions. We conclude that the two networks share many similarities and some differences. Notably, both structures tend to be influenced by the clustering of directors on boards, more than by the accumulation of board seats by individual directors; that shared multiple board memberships (multiple interlocks) are an important feature of both infrastructures, detracting from global connectivity (but more so in the Australian case); and that company structural power may be relatively more diffuse in the US structure than in Australia.

interlocking directors bipartite graphs small world global network structure 


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  1. Albert, R. and A.-L. Barabàsi (2002), “Statistical Mechanics of Complex Networks,” Review of Modern Physics, 74, 47–97.Google Scholar
  2. Albert, R., H. Jeong and A.-L. Barabàsi (1999), “Diameter of the World Wide Web,” Nature, 401, 130–131.Google Scholar
  3. Alexander, M. (2002), “The Small World of the Corporate Elite: The US and Australia,” Paper presented at Sunbelt International Social Network Conference, New Orleans, Feb. 2002.Google Scholar
  4. Alexander, M. (2003), “Boardroom Networks Among Australian Directors, 1976 and 1996: The Impact of Investor Capitalism,” Journal of Sociology, 39, 231–251.Google Scholar
  5. Allen, M.P. (1974), “The Structure of Interorganizational Elite Cooptation,” American Sociological Review, 39, 393–406.Google Scholar
  6. Borgatti, S.P. and M.G. Everett (1997), “Network Analysis of 2-Mode Data,” Social Networks, 19, 243–269.Google Scholar
  7. Boyd, J.P. and K.J. Joans (2001), “Are Social Equivalences Ever Regular? Permutation and Exact Tests,” Social Networks, 23, 87–123.Google Scholar
  8. Breiger, R.L. (1974), “The Duality of Persons and Groups,” Social Forces, 53, 181–190.Google Scholar
  9. Breiger, R.L. and P. Pattison (1986), “Cumulated Social Roles: The Duality of Persons and Their Algebras,” Social Networks,8,215–256.Google Scholar
  10. Buchanan, M. (2002), Nexus: Small Worlds and the Groundbreaking Science of Networks.New York: W.W. Norton.Google Scholar
  11. Carroll, W.K. and M. Alexander (1999), “Finance Capital and Capitalist Class Integration in the 1990s: Networks of Interlocking Directorships in Canada and Australia,” The Canadian Review of Sociology and Anthropology, 36, 331–354.Google Scholar
  12. Castles, F.G. (1991), “Why Compare Australia?” in F.G. Castles (Ed.), Australia Compared: People, Policies and Politics, Sydney: Allen and Unwin, pp. 1–14.Google Scholar
  13. Davis, A.B. Gardner and M.R. Gardner (1941), Deep South. Chicago: University of Chicago Press.Google Scholar
  14. Davis, G.F. and M.S. Mizruchi (1999), “The Money Centre Cannot Hold: Commercial Banks in the U.S. System of Corporate Governance,” Administrative Science Quarterly, 44, 215–239.Google Scholar
  15. Erdös, P. and A. Renyi (1959), “On Random Graphs. I,” Publicationes Mathematicae (Debrecen),6,290–297.Google Scholar
  16. Fararo, T.J. and P. Doreian (1984), “Tripartite Structural Analysis: Generalizing the Breiger-Wilson Formalism,” Social Networks,6,141–175.Google Scholar
  17. Feld, S. (1981), “The Focused Organization of Social Ties,” American Journal of Sociology, 86, 1015–1035.Google Scholar
  18. Frank, O. (1981), “A Survey of Statistical Methods for Graph Analysis,” in S. Leinhardt (Ed.), Sociological Methodology. San Francisco: Jossey-Bass, pp. 110–155.Google Scholar
  19. Frank, O. and K. Nowicki (1993), “Exploratory Statistical Analysis of Networks,” in J. Gimbel, J.W. Kennedy and L.V. Quintas (Eds.), Quo Vadis, Graph Theory? Annals of Discrete Mathematics,vol. 55, pp. 349–366.Google Scholar
  20. Frank, O. and D. Strauss (1986), “Markov Graphs,” Journal of the American Statistical Association, 81, 832–842.Google Scholar
  21. Galaskiewicz, J. (1985), Social Organization of an Urban Grants Economy.New York: Academic Press.Google Scholar
  22. Granovetter, M. (1973), “The Strength of Weak Ties,” American Journal of Sociology, 78, 1360–1380.Google Scholar
  23. Guare, J. (1990), Six Degrees of Separation: A Play.New York: Vintage.Google Scholar
  24. Iacobucci, D. and S. Wasserman(1990), “Social Networks with Two Sets of Actors,” Psychometrika, 55, 707–720.Google Scholar
  25. Kochen, M. (1989), The Small World, Norwood, NJ: Ablex.Google Scholar
  26. Milgram, S. (1967), “The Small World Problem,” Psychology Today,2,60–67.Google Scholar
  27. Mintz, B. and M. Schwartz (1985), The Power Structure of American Business. Chicago: University of Chicago Press.Google Scholar
  28. Mische, A. and H.C. White (1998), “Between Conversation and Situation: Public Switching Dynamics Across Network Domains,” Social Research, 65, 695–724.Google Scholar
  29. Mizruchi, M.S. (1996), “What do Interlocks do? AnAnalysis, Critique, and Assessment of Research on Interlocking Directorates,” Annual Review of Sociology, 22, 271–298.Google Scholar
  30. Newman, M.E.J. (2001a), “Scientific Collaboration Networks. I. Network Construction and Fundamental Results,” Physical Review E, 64, 016131.Google Scholar
  31. Newman, M.E.J. (2001b), “Scientific Collaboration Networks. II. Shortest Paths, Weighted Networks, and Centrality,” Physical Review E, 64, 016132.Google Scholar
  32. Newman, M.E.J., S.H. Strogatz and D.J. Watts (2001), “Random Graphs with Arbitrary Degree Distributions and their Applications,” Physical Review E, 64, 026118.Google Scholar
  33. Ornstein, M.D. (1982), “Interlocking Directorates in Canada: Evidence from Replacement Patterns,” Social Science Research,4,3–25.Google Scholar
  34. Ornstein, M.D. (1984), “Interlocking Directorates in Canada: Intercorporate or Class Alliance?” Administrative Science Quarterly, 29, 210–232.Google Scholar
  35. Palmer, D. (1983), “Broken Ties: Interlocking Directorates and Intercorporate Coordination,” Administrative Science Quarterly, 28, 40–55.Google Scholar
  36. Pattison, P.E. and G.L. Robins (2002), “Neighborhood Based Models for Social Networks,” Sociological Methodology, 32, 301–337.Google Scholar
  37. Pattison, P.E., S. Wasserman, G.L. Robins, and A. Kanfer (2000), “Statistical Evaluation of Algebraic Constraints for Social Networks,” Journal of Mathematical Psychology, 44, 536–568.Google Scholar
  38. Pennings, J.M. (1980), Interlocking Directorates. San Francisco: Jossey-Bass.Google Scholar
  39. Robins, G.L. (2003), “The Small Worlds of Small Social Networks,” Paper presented at the American Association for the Advancement of Science Annual Meeting, Denver, CO, 13–18 Feb.Google Scholar
  40. Robins, G.L., P.E. Pattison and J. Woolcock (in press), “Small and Other Worlds: Global Network Structures from Local Processes,” American Journal of Sociology.Google Scholar
  41. Scott, J. (1997), Corporate Business and Capitalist Classes.New York: Oxford University Press.Google Scholar
  42. Skvoretz, J. and K. Faust (1999), “Logit Models for Affiliation Networks,” Sociological Methodology, 29, 253–280.Google Scholar
  43. Snijders, T.A.B. and F. Stokman (1987), “Extension of Triad Counts to Networks with Different Subsets of Points and Testing Underlying Graph Distributions,” Social Networks,9,249–275.Google Scholar
  44. Snijders, T.A.B. and M.A.J. van Duijn (2002), “Conditional Maximum Likelihood Estimation Under Various Specifications of Exponential Random Graph Models,” in Jan Hagberg (Ed.), Contributions to Social Network.Analysis, Information Theory, and Other Topics in Statistics: A Festschrift in Honour of Ove Frank, University of Stockholm: Department of Statistics, pp. 117–134.Google Scholar
  45. Stokman, F.N., R. Ziegler and J. Scott (1985), Networks of Corporate Power. Cambridge, Polity Press.Google Scholar
  46. Strogatz, S.H. (2001), “Exploring Complex Networks,” Nature, 410, 268–276.Google Scholar
  47. Useem, M. (1984), The Inner Circle: Large Corporation and the Rise of Business Political Activity in the U.S.and U.K.New York: Oxford University Press.Google Scholar
  48. Wasserman, S. and D. Iacobucci (1991), “Statistical Modeling of One-Mode and Two-Mode Networks: Simultaneous Analysis of Graphs and Bipartite Graphs,” British Journal of Mathematical and Statistical Psychology, 44, 13–43.Google Scholar
  49. Wasserman, S. and P.E. Pattison (1996), “Logit Models and Logistic Regressions for Social Networks, I. An Introduction to Markov Random Graphs and P*, Psychometrika, 60, 401–425.Google Scholar
  50. Wasserman, S. and G.L. Robins (in press), “An Introduction to Random Graphs, Dependence Graphs, and p,” in P. Carrington, J. Scott and S. Wasserman (Eds.), Models and Methods in Social Network Analysis, Cambridge University Press, forthcoming.Google Scholar
  51. Watts, D.J. (1999a), Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton, NJ: Princeton University Press.Google Scholar
  52. Watts, D.J. (1999b), “Networks, Dynamics, and the Small-World Phenomenon,” American Journal of Sociology, 105, 493–527.Google Scholar
  53. Watts, D.J., P.S. Dodds and M.E.J. Newman (2002), “Identity and Search in Social Networks,” Science, 296, 1302–1305.Google Scholar
  54. Watts, D.J. and S.H. Strogatz (1998), “Collective Dynamics of 'small World' Networks,” Nature, 393, 440–442.PubMedGoogle Scholar
  55. White, H.C. (1995), “Network Switchings and Bayesian Forks: Reconstructing the Social and Behavioral Sciences,” Social Research, 62, 1035–1063.Google Scholar
  56. Windolf, P. (2002), Corporate Networks in Europe and the United States. Oxford; NewYork, NY, Oxford University Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Garry Robins
    • 1
  • Malcolm Alexander
    • 2
  1. 1.Department of PsychologyUniversity of MelbourneVictoriaAustralia.
  2. 2.School of Arts, Media and CultureGriffith UniversityAustralia.

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