Data Mining and Knowledge Discovery

, Volume 32, Issue 5, pp 1421–1443 | Cite as

Social centrality using network hierarchy and community structure

  • Rakhi SaxenaEmail author
  • Sharanjit Kaur
  • Vasudha Bhatnagar
Part of the following topical collections:
  1. Journal Track of ECML PKDD 2018


Several centrality measures have been formulated to quantify the notion of ‘importance’ of actors in social networks. Current measures scrutinize either local or global connectivity of the nodes and have been found to be inadequate for social networks. Ignoring hierarchy and community structure, which are inherent in all human social networks, is the primary cause of this inadequacy. Positional hierarchy and embeddedness of an actor in the community are intuitively crucial determinants of his importance. The theory of social capital asserts that an actor’s importance is derived from his position in network hierarchy as well as from the potential to mobilize resources through intra-community (bonding) and inter-community (bridging) ties. Inspired by this idea, we propose a novel centrality measure social centrality (SC) for actors in social networks. Our measure accounts for—(1) an individual’s propensity to socialize, and (2) his connections within and outside the community. These two factors are suitably aggregated to produce social centrality score. Comparative analysis of SC measure with classical and recent centrality measures using large public networks shows that it consistently produces more realistic ranking of nodes. The inference is based on the available ground truth for each tested networks. Extensive analysis of rankings delivered by SC measure and mapping with known facts in well-studied networks justifies its effectiveness in diverse social networks. Scalability evaluation of SC measure justifies its efficacy for real-world large networks.


Centrality Social capital Hierarchy Community Strength of ties k-Truss decomposition 



  1. Adler PS, Kwon SW (2002) Social capital: prospects for a new concept. Acad Manag Rev 27(1):17–40CrossRefGoogle Scholar
  2. Alvarez-Hamelin JI, Barrat A, Vespignani A (2006) Large scale networks fingerprinting and visualization using the k-core decomposition. Adv Neural Inf Process Syst 18:41–50Google Scholar
  3. Alvarez-Hamelin JI, Dall’Asta L, Barrat A, Vespignani A (2008) k-core decomposition of internet graphs: hierarchies, self-similarity and measurement biases. Netw Heterog Med 3(2):371MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bakman L, Oliver AL (2014) Coevolutionary perspective of industry network dynamics, vol 1. Emerald Group Publishing Ltd., Bingley, pp 3–36Google Scholar
  5. Bloch F, Jackson MO, Tebaldi P (2017) Centrality measures in networks. Available at SSRN:
  6. Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech.
  7. Boldi P, Vigna S (2014) Axioms for centrality. Internet Math 10(3–4):222–262MathSciNetCrossRefGoogle Scholar
  8. Borgatti SP, Everett MG (2006) A graph-theoretic perspective on centrality. Soc Netw 28(4):466–484CrossRefGoogle Scholar
  9. Burt RS (2001) Structural Holes versus network closure as social capital. In: Social capital: theory and research. Aldine de Gruyter, NY, USA, pp 31–56Google Scholar
  10. Cohen J (2008) Trusses: cohesive subgraphs for social network analysis. NSA: Technical reportGoogle Scholar
  11. David E, Jon K (2010) Networks, crowds, and markets: reasoning about a highly connected world. Cambridge University Press, New YorkzbMATHGoogle Scholar
  12. Freeman LC (1979) Centrality in social networks: conceptual clarification. Soc Netw 1(3):215–239MathSciNetCrossRefGoogle Scholar
  13. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. PNAS 99(12):7821–7826MathSciNetCrossRefzbMATHGoogle Scholar
  14. Granovetter MS (1973) The strength of weak ties. Am J Soc 78(6):1360–1380CrossRefGoogle Scholar
  15. Gupta N, Singh A, Cherifi H (2016) Centrality measures for networks with community structure. Phys A 452:46–59CrossRefGoogle Scholar
  16. Ilyas MU, Radha H (2010) A KLT-inspired node centrality for identifying influential neighborhoods in graphs. In: Proceedings of 44th annual conference on information sciences and systems, pp 1–7Google Scholar
  17. Kang U, Papadimitriou S, Sun J, Tong H (2011) Centralities in large networks: algorithms and observations. In: Proceedings of SIAM international conference on data mining, pp 119–130. ISBN 978-0-898719-92-5Google Scholar
  18. Koschade SA (2006) A social network analysis of Jemaah Islamiyah: the applications to counter-terrorism and intelligence. Stud Confl Terror 29(6):559–575CrossRefGoogle Scholar
  19. Landherr A, Friedl B, Heidemann J (2010) A critical review of centrality measures in social networks. Bus Inf Syst Eng 2(6):371–385CrossRefGoogle Scholar
  20. Li C, Li Q, Mieghem PV, Stanley HE, Wang H (2015) Correlation between centrality metrics and their application to the opinion model. Eur Phys J B 88(3):65MathSciNetCrossRefGoogle Scholar
  21. Lin N (2008) A network theory of social capital. The handbook of social capital, vol 2. Oxford University Press, Oxford, pp 50–69Google Scholar
  22. Nahapiet J, Ghoshal S (1998) Social capital, intellectual capital, and the organizational advantage. Acad Manag Rev 23(2):242–266CrossRefGoogle Scholar
  23. Nick B, Lee C, Cunningham P, Brandes U (2013) Simmelian backbones: amplifying hidden homophily in facebook networks, In: Proceedings of IEEE/ACM international conference on advances in social networks analysis and mining, pp 525–532Google Scholar
  24. Ortmann M, Brandes U (2014) Triangle listing algorithms: back from the diversion. In: Proceedings of the sixteenth workshop on algorithm engineering and experiments (ALENEX), pp 1–8Google Scholar
  25. Phillip B (1987) Power and centrality: a family of measures. Am J Soc 92(5):1170–1182CrossRefGoogle Scholar
  26. Putnam RD (2002) Democracies in flux: the evolution of social capital in contemporary society. Oxford University Press, New YorkCrossRefGoogle Scholar
  27. Qi X, Duval RD, Christensen K, Fuller E, Spahiu A, Wu Q, Wu Y, Tang W, Zhang C (2013) Terrorist networks, network energy and node removal: a new measure of centrality based on Laplacian energy. Soc Netw 2:19–31CrossRefGoogle Scholar
  28. Qi X, Fuller E, Luo R, Zhang C (2015) A novel centrality method for weighted networks based on the Kirchhoff polynomial. Pattern Recogn Lett 58:51–60CrossRefGoogle Scholar
  29. Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D (2004) Defining and identifying communities in networks. Proc Nat Acad Sci 101(9):2658–2663CrossRefGoogle Scholar
  30. Shi X, Adamic LA, Strauss MJ (2007) Networks of strong ties. Phys A 378(1):33–47CrossRefGoogle Scholar
  31. Subbian K, Sharma D, Wen Z, Srivastava J (2013) Finding influencers in networks using social capital. In: Proceedings of IEEE/ACM international conference on advances in social networks analysis and miningGoogle Scholar
  32. Valente TW, Coronges K, Lakon C, Costenbader E (2008) How correlated are network centrality measures? Connections 28(1):16–26Google Scholar
  33. Wang J, Cheng J (2012) Truss decomposition in massive networks. Proc VLDB Endow 5(9):812–823CrossRefGoogle Scholar
  34. Wang M, Wang C, Yu JX, Zhang J (2015) Community detection in social networks: an in-depth benchmarking study with a procedure-oriented framework. Proc VLDB Endow 8(10):998–1009CrossRefGoogle Scholar
  35. Xie J, Szymanski BK (2013) LabelRank: a stabilized label propagation algorithm for community detection in networks. In: Proceedings of the 2nd IEEE network science workshop, pp 138–143Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Deshbandhu CollegeUniversity of DelhiNew DelhiIndia
  2. 2.Acharya Narendra Dev CollegeUniversity of DelhiNew DelhiIndia
  3. 3.Department of Computer ScienceUniversity of DelhiNew DelhiIndia

Personalised recommendations