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Social centrality using network hierarchy and community structure

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Abstract

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.

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Notes

  1. We experimented with various community detection algorithms available in the Python igraph library, and chose the Multilevel algorithm because it was the fastest.

  2. Weighted versions of classical centrality measures were used from the Python igraph library; Python code for implemented measures and datasets used for experimentation are available at https://github.com/rakhisaxena/SocialCentrality.

  3. http://www.kddcup2012.org/wcukierski/enron-email-dataset.

  4. STC ran out of memory and SoCap did not complete even after running for a day.

  5. Enron employee position in organization structure obtained from http://www.infosys.tuwien.ac.at/staff/dschall/email/enron-employees.txt.

  6. https://www.cs.cornell.edu/projects/kddcup/datasets.html

  7. https://aminer.org/DBLP_Citation.

  8. http://www.nber.org/patents/.

  9. http://www.entrepreneur.com/article/185660.

  10. http://usatoday30.usatoday.com/money/industries/technology/maney/2005-12-13-patent_x.htm.

  11. Synthetic networks generated using igraph package; ER: erdos.renyi.game (n, m \(=\) 2n); WS: watts.strogatz.game (n, dim \(=\) 1, nei \(=\) 4, \(p=0.3\)); FF: forest.fire.game(n, ambs \(=\) 4, bw.factor \(=\) 0.2, fw.prob \(=\) 0.3)

  12. Real-world networks downloaded from http://www.snap.edu/data.

References

  • Adler PS, Kwon SW (2002) Social capital: prospects for a new concept. Acad Manag Rev 27(1):17–40

    Article  Google Scholar 

  • Alvarez-Hamelin JI, Barrat A, Vespignani A (2006) Large scale networks fingerprinting and visualization using the k-core decomposition. Adv Neural Inf Process Syst 18:41–50

    Google Scholar 

  • 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):371

    Article  MathSciNet  MATH  Google Scholar 

  • Bakman L, Oliver AL (2014) Coevolutionary perspective of industry network dynamics, vol 1. Emerald Group Publishing Ltd., Bingley, pp 3–36

    Google Scholar 

  • Bloch F, Jackson MO, Tebaldi P (2017) Centrality measures in networks. Available at SSRN: https://ssrn.com/abstract=2749124

  • Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech. https://doi.org/10.1088/1742-5468/2008/10/P10008

  • Boldi P, Vigna S (2014) Axioms for centrality. Internet Math 10(3–4):222–262

    Article  MathSciNet  Google Scholar 

  • Borgatti SP, Everett MG (2006) A graph-theoretic perspective on centrality. Soc Netw 28(4):466–484

    Article  Google Scholar 

  • Burt RS (2001) Structural Holes versus network closure as social capital. In: Social capital: theory and research. Aldine de Gruyter, NY, USA, pp 31–56

  • Cohen J (2008) Trusses: cohesive subgraphs for social network analysis. NSA: Technical report

  • David E, Jon K (2010) Networks, crowds, and markets: reasoning about a highly connected world. Cambridge University Press, New York

    MATH  Google Scholar 

  • Freeman LC (1979) Centrality in social networks: conceptual clarification. Soc Netw 1(3):215–239

    Article  MathSciNet  Google Scholar 

  • Girvan M, Newman MEJ (2002) Community structure in social and biological networks. PNAS 99(12):7821–7826

    Article  MathSciNet  MATH  Google Scholar 

  • Granovetter MS (1973) The strength of weak ties. Am J Soc 78(6):1360–1380

    Article  Google Scholar 

  • Gupta N, Singh A, Cherifi H (2016) Centrality measures for networks with community structure. Phys A 452:46–59

    Article  Google Scholar 

  • 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 1–7

  • 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 978-0-898719-92-5

  • Koschade SA (2006) A social network analysis of Jemaah Islamiyah: the applications to counter-terrorism and intelligence. Stud Confl Terror 29(6):559–575

    Article  Google Scholar 

  • Landherr A, Friedl B, Heidemann J (2010) A critical review of centrality measures in social networks. Bus Inf Syst Eng 2(6):371–385

    Article  Google Scholar 

  • 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):65

    Article  MathSciNet  Google Scholar 

  • Lin N (2008) A network theory of social capital. The handbook of social capital, vol 2. Oxford University Press, Oxford, pp 50–69

    Google Scholar 

  • Nahapiet J, Ghoshal S (1998) Social capital, intellectual capital, and the organizational advantage. Acad Manag Rev 23(2):242–266

    Article  Google Scholar 

  • 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 525–532

  • 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 1–8

  • Phillip B (1987) Power and centrality: a family of measures. Am J Soc 92(5):1170–1182

    Article  Google Scholar 

  • Putnam RD (2002) Democracies in flux: the evolution of social capital in contemporary society. Oxford University Press, New York

    Book  Google Scholar 

  • 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 2:19–31

    Article  Google Scholar 

  • Qi X, Fuller E, Luo R, Zhang C (2015) A novel centrality method for weighted networks based on the Kirchhoff polynomial. Pattern Recogn Lett 58:51–60

    Article  Google Scholar 

  • Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D (2004) Defining and identifying communities in networks. Proc Nat Acad Sci 101(9):2658–2663

    Article  Google Scholar 

  • Shi X, Adamic LA, Strauss MJ (2007) Networks of strong ties. Phys A 378(1):33–47

    Article  Google Scholar 

  • 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 mining

  • Valente TW, Coronges K, Lakon C, Costenbader E (2008) How correlated are network centrality measures? Connections 28(1):16–26

    Google Scholar 

  • Wang J, Cheng J (2012) Truss decomposition in massive networks. Proc VLDB Endow 5(9):812–823

    Article  Google Scholar 

  • 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):998–1009

    Article  Google Scholar 

  • 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 138–143

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Authors and Affiliations

  1. Deshbandhu College, University of Delhi, New Delhi, India

    Rakhi Saxena

  2. Acharya Narendra Dev College, University of Delhi, New Delhi, India

    Sharanjit Kaur

  3. Department of Computer Science, University of Delhi, New Delhi, India

    Vasudha Bhatnagar

Authors
  1. Rakhi Saxena
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  2. Sharanjit Kaur
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  3. Vasudha Bhatnagar
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Correspondence to Rakhi Saxena.

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Responsible editors: Jesse Davis, Elisa Fromont, Derek Greene, Björn Bringmann.

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Saxena, R., Kaur, S. & Bhatnagar, V. Social centrality using network hierarchy and community structure. Data Min Knowl Disc 32, 1421–1443 (2018). https://doi.org/10.1007/s10618-018-0582-x

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