Journal of Statistical Physics

, Volume 151, Issue 3–4, pp 745–764 | Cite as

Social Cohesion, Structural Holes, and a Tale of Two Measures



In the social sciences, the debate over the structural foundations of social capital has long vacillated between two positions on the relative benefits associated with two types of social structures: closed structures, rich in third-party relationships, and open structures, rich in structural holes and brokerage opportunities. In this paper, we engage with this debate by focusing on the measures typically used for formalising the two conceptions of social capital: clustering and effective size. We show that these two measures are simply two sides of the same coin, as they can be expressed one in terms of the other through a simple functional relation. Building on this relation, we then attempt to reconcile closed and open structures by proposing a new measure, Simmelian brokerage, that captures opportunities of brokerage between otherwise disconnected cohesive groups of contacts. Implications of our findings for research on social capital and complex networks are discussed.


Social networks Social capital Social cohesion Structural holes Clustering Effective size Simmelian brokerage 


  1. 1.
    Ahuja, G.: Collaboration networks, structural holes, and innovation: a longitudinal study. Adm. Sci. Q. 45, 425–455 (2000) CrossRefGoogle Scholar
  2. 2.
    Aral, S., Van Alstyne, M.: The diversity-bandwidth trade-off. Am. J. Sociol. 117(1), 90–171 (2011) CrossRefGoogle Scholar
  3. 3.
    Barrat, A., Barthélemy, M., Pastor-Satorras, R., Vespignani, A.: The architecture of complex weighted networks. Proc. Natl. Acad. Sci. USA 101, 3747–3752 (2004) ADSCrossRefGoogle Scholar
  4. 4.
    Baum, J.A.C., McEvily, B., Rowley, T.J.: Better with age? Tie longevity and the performance implications of bridging and closure. Organ. Sci. 23, 529–546 (2012) CrossRefGoogle Scholar
  5. 5.
    Borgatti, S.P.: Structural holes: unpacking Burt’s redundancy measures. Connections 20, 35 (1997) Google Scholar
  6. 6.
    Brass, D.J.: It’s all in your social network. In: Ford, C.M., Gioia, D.A. (eds.) Creative Action in Organizations, pp. 94–98. Sage, Thousand Oaks (1995) Google Scholar
  7. 7.
    Burt, R.S.: Structural Holes. The Social Structure of Competition. Harvard University Press, Cambridge (1992) Google Scholar
  8. 8.
    Burt, R.S.: The gender of social capital. Ration. Soc. 10, 5–46 (1998) CrossRefGoogle Scholar
  9. 9.
    Burt, R.S.: Structural holes and good ideas. Am. J. Sociol. 110, 349–399 (2004) CrossRefGoogle Scholar
  10. 10.
    Burt, R.S.: Brokerage and Closure. Oxford University Press, Oxford (2005) Google Scholar
  11. 11.
    Burt, R.S.: Neighbor Networks. Oxford University Press, Oxford (2010) Google Scholar
  12. 12.
    Burt, R.S., Knez, M.: Kinds of third-party effects on trust. Ration. Soc. 7, 255–292 (1995) CrossRefGoogle Scholar
  13. 13.
    Centola, D., Macy, M.W.: Complex contagion and the weakness of long ties. Am. J. Sociol. 113, 702–734 (2007) CrossRefGoogle Scholar
  14. 14.
    Coleman, J.S.: Social capital in the creation of human capital. Am. J. Sociol. 94, S95–S120 (1988) CrossRefGoogle Scholar
  15. 15.
    Coleman, J.S.: Foundations of Social Theory. Harvard University Press, Cambridge (1990) Google Scholar
  16. 16.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991) MATHCrossRefGoogle Scholar
  17. 17.
    Davis, J.A.: Clustering and hierarchy in interpersonal relations: testing two graph theoretical models on 742 sociomatrices. Am. Sociol. Rev. 35(5), 843–851 (1970) CrossRefGoogle Scholar
  18. 18.
    Davis, J.A., Holland, P.W., Leinhardt, S.: Comments on Professor Mazur’s hypothesis about interpersonal sentiments. Am. Sociol. Rev. 36, 309–311 (1971) CrossRefGoogle Scholar
  19. 19.
    Dekker, D.: Measures of Simmelian tie strength, Simmelian brokerage, and Simmelianly brokered. J. Soc. Struct. 7(1), 1–22 (2006) ADSGoogle Scholar
  20. 20.
    Fleming, L., Mingo, S., Chen, D.: Collaborative brokerage, generative creativity, and creative success. Adm. Sci. Q. 52, 443–475 (2007) Google Scholar
  21. 21.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486, 75–174 (2010) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Friedkin, N.E.: Social cohesion. Annu. Rev. Sociol. 30, 409–425 (2004) CrossRefGoogle Scholar
  23. 23.
    Gargiulo, M., Benassi, M.: Trapped in your own net? Network cohesion, structural holes, and the adaptation of social capital. Organ. Sci. 11, 183–196 (2000) CrossRefGoogle Scholar
  24. 24.
    Gargiulo, M., Ertug, G., Galunic, C.: The two faces of control: network closure and individual performance among knowledge workers. Adm. Sci. Q. 54, 299–333 (2009) CrossRefGoogle Scholar
  25. 25.
    Gould, R.V.: Multiple networks and mobilization in the Paris Commune, 1871. Am. Sociol. Rev. 56, 716–729 (1991) CrossRefGoogle Scholar
  26. 26.
    Granovetter, M.: The strength of weak ties. Am. J. Sociol. 78, 1360–1380 (1973) CrossRefGoogle Scholar
  27. 27.
    Granovetter, M.: The impact of social structure on economic outcomes. J. Econ. Perspect. 19(1), 33–50 (2005) CrossRefGoogle Scholar
  28. 28.
    Hansen, M.T.: The search-transfer problem: the role of weak ties in sharing knowledge across organization subunits. Adm. Sci. Q. 44, 232–248 (1999) CrossRefGoogle Scholar
  29. 29.
    Holland, P.W., Leinhardt, S.: A method for detecting structure in sociometric data. Am. J. Sociol. 76, 492–513 (1970) CrossRefGoogle Scholar
  30. 30.
    Holland, P.W., Leinhardt, S.: Transitivity in structural models of small groups. Comp. Group Stud. 2, 107–124 (1971) Google Scholar
  31. 31.
    Holme P., Kim, B.J.: Growing scale-free networks with tunable clustering. Phys. Rev. E 65, 026107 (2002) ADSCrossRefGoogle Scholar
  32. 32.
    Holme, P., Park, S.M., Kim, B.J., Edling, C.R.: Korean university life in a network perspective: dynamics of a large affiliation network. Phys. A, Stat. Mech. Appl. 373, 821–830 (2007) CrossRefGoogle Scholar
  33. 33.
    Ingram, P., Roberts, P.W.: Friendships among competitors in the Sydney hotel industry. Am. J. Sociol. 106(2), 387–423 (2000) CrossRefGoogle Scholar
  34. 34.
    Krackhardt, D.: Simmelian tie: super strong and sticky. In: Kramer, R.M., Neale, M.A. (eds.) Power and Influence in Organizations, pp. 21–38. Sage, Thousand Oaks (1998) Google Scholar
  35. 35.
    Krackhardt, D.: The ties that torture: Simmelian tie analysis in organizations. Res. Sociol. Organ. 16, 183–210 (1999) Google Scholar
  36. 36.
    Krackhardt, D., Kilduff, M.: Structure, culture and Simmelian ties in entrepreneurial firms. Soc. Netw. 24, 279–290 (2002) CrossRefGoogle Scholar
  37. 37.
    Lambiotte, R., Panzarasa, P.: Communities, knowledge creation, and information diffusion. J. Informetr. 3(3), 180–190 (2009) CrossRefGoogle Scholar
  38. 38.
    Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001) ADSCrossRefGoogle Scholar
  39. 39.
    Latora, V., Marchiori, M.: Economic behavior of small-world networks. Eur. Phys. J. B 32, 249–263 (2003) ADSCrossRefGoogle Scholar
  40. 40.
    Lin, N.: Social Capital. A Theory of Social Structure and Action. Cambridge University Press, New York (2001) CrossRefGoogle Scholar
  41. 41.
    Lin, N., Cook, K., Burt, R.S. (eds.): Social Capital. Theory and Research. Aldine Transaction, New Brunswick and London (2001) Google Scholar
  42. 42.
    Long Lingo, E., O’Mahony, S.: Nexus work: brokerage on creative projects. Adm. Sci. Q. 55, 47–81 (2010) CrossRefGoogle Scholar
  43. 43.
    Luce, R.D., Perry, A.D.: A method of matrix analysis of group structure. Psychometrika 14(1), 95–116 (1949) MathSciNetCrossRefGoogle Scholar
  44. 44.
    Mizruchi, M., Stearns, L.B.: Getting deals done: the use of social networks in bank decision-making. Am. Sociol. Rev. 66, 647–671 (2001) CrossRefGoogle Scholar
  45. 45.
    Nahapiet, J., Ghoshal, S.: Social capital, intellectual capital, and the organizational advantage. Acad. Manag. Rev. 23, 242–266 (1998) Google Scholar
  46. 46.
    Obstfeld, D.: Social networks, the tertius iungens orientation, and involvement in innovation. Adm. Sci. Q. 50, 100–130 (2005) Google Scholar
  47. 47.
    Onnela, J.-P., Saramäki, J., Kertész, J., Kaski, K.: Intensity and coherence of motifs in weighted complex networks. Phys. Rev. E 71, 065103 (2005) ADSCrossRefGoogle Scholar
  48. 48.
    Opsahl, T., Panzarasa, P.: Clustering in weighted networks. Soc. Netw. 31, 155–163 (2009) CrossRefGoogle Scholar
  49. 49.
    Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 814–818 (2005) ADSCrossRefGoogle Scholar
  50. 50.
    Perry-Smith, J.E.: Social yet creative: the role of social relationships in facilitating individual creativity. Acad. Manag. J. 49, 85–101 (2006) CrossRefGoogle Scholar
  51. 51.
    Podolny, J.M., Baron, J.N.: Resources and relationships: social networks and mobility in the workplace. Am. Sociol. Rev. 62, 673–693 (1997) CrossRefGoogle Scholar
  52. 52.
    Ravasz, E., Barabási, A.-L.: Hierarchical organization in complex networks. Phys. Rev. E 67, 026112 (2003) ADSCrossRefGoogle Scholar
  53. 53.
    Reagans, R., McEvily, B.: Network structure and knowledge transfer: the effects of cohesion and range. Adm. Sci. Q. 48, 240–267 (2003) CrossRefGoogle Scholar
  54. 54.
    Reagans, R., Zuckerman, E.: Networks, diversity and performance: the social capital of R&D units. Organ. Sci. 12, 502–517 (2001) CrossRefGoogle Scholar
  55. 55.
    Rodan, S., Galunic, C.: More than network structure: how knowledge heterogeneity influences managerial performance and innovativeness. Strateg. Manag. J. 25, 541–562 (2004) CrossRefGoogle Scholar
  56. 56.
    Saramäki, J., Kivelä, M., Onnela, J.-P., Kaski, K., Kertész, J.: Generalizations of the clustering coefficient to weighted complex networks. Phys. Rev. E 75, 027105 (2007) ADSCrossRefGoogle Scholar
  57. 57.
    Serrano, M.A., Boguñá, M.: Tuning clustering in random networks with arbitrary degree distributions. Phys. Rev. E 72, 036133 (2005) ADSCrossRefGoogle Scholar
  58. 58.
    Simmel, G.: The Sociology of Georg Simmel. Lightning Source, Milton Keynes ([1923] 2011). Trans. by K.H. Wolff Google Scholar
  59. 59.
    Sosa, M.E.: Where do creative interactions come from? The role of tie content and social networks. Organ. Sci. 22, 1–21 (2011) CrossRefGoogle Scholar
  60. 60.
    Stovel, K., Shaw, L.: Brokerage. Annu. Rev. Sociol. 38, 139–158 (2012) CrossRefGoogle Scholar
  61. 61.
    Tortoriello, M., Krackhardt, D.: Activating cross-boundary knowledge: the role of Simmelian ties in the generation of innovations. Acad. Manag. J. 53(1), 167–181 (2010) CrossRefGoogle Scholar
  62. 62.
    Tortoriello, M., Reagans, R., McEvily, B.: Bridging the knowledge gap: the influence of strong ties, network cohesion, and network range on the transfer of knowledge between organizational units. Organ. Sci. 23, 1024–1039 (2012) CrossRefGoogle Scholar
  63. 63.
    Uzzi, B.: Social structure and competition in interfirm networks: the paradox of embeddedness. Adm. Sci. Q. 43, 35–67 (1997) CrossRefGoogle Scholar
  64. 64.
    Uzzi, B., Spiro, J.: Collaboration and creativity: the small world problem. Am. J. Sociol. 111, 447–504 (2005) CrossRefGoogle Scholar
  65. 65.
    Vázquez, A.: Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations. Phys. Rev. E 67, 056104 (2003) ADSCrossRefGoogle Scholar
  66. 66.
    Vázquez, A., Pastor-Satorras, R., Vespignani, A.: Large-scale topological and dynamical properties of the Internet. Phys. Rev. E 65, 066130 (2002) ADSCrossRefGoogle Scholar
  67. 67.
    Vedres, B., Stark, D.: Structural folds: generative disruption in overlapping groups. Am. J. Sociol. 115(4), 1150–1190 (2010) CrossRefGoogle Scholar
  68. 68.
    Watts, D.J.: Small Worlds: The Dynamics of Networks Between Order and Randomness. Princeton University Press, Princeton (1999) Google Scholar
  69. 69.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440 (1998) ADSCrossRefGoogle Scholar
  70. 70.
    Zhang, B., Horvath, S.: A general framework for weighted gene co-expression network analysis. Stat. Appl. Genet. Mol. Biol. 4, 17 (2005) MathSciNetGoogle Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  2. 2.School of Business and ManagementQueen Mary University of LondonLondonUK

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