Advertisement

Central Positions in Social Networks

  • Ulrik BrandesEmail author
Conference paper
  • 100 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12159)

Abstract

This contribution is an overview of our recent work on the concept of centrality in networks. Instead of proposing new centrality indices, providing faster algorithms, or presenting new rules for when an index can be classified as a centrality, this research shifts the focus to the more elementary question whether a node is in a more central position than another. Viewing networks as data on overlapping dyads, and defining the position of a node as the whole of its relationships to the rest of the network, we obtain a very general procedure for doing centrality analysis; not only on social networks but networks from all kinds of domains. Our framework further suggests a variety of computational challenges.

Keywords

Data science Social networks Centrality Algorithmics 

References

  1. 1.
    Bloch, F., Jackson, M.O., Tebaldi, P.: Centrality measures in networks. SSRN Electron. J. (2019).  https://doi.org/10.2139/ssrn.2749124CrossRefGoogle Scholar
  2. 2.
    Boldi, P., Vigna, S.: Axioms for centrality. Internet Math. 10(3–4), 222–262 (2014).  https://doi.org/10.1080/15427951.2013.865686MathSciNetCrossRefGoogle Scholar
  3. 3.
    Borgatti, S.P.: Centrality and network flow. Soc. Netw. 27(1), 55–71 (2005).  https://doi.org/10.1016/j.socnet.2004.11.008MathSciNetCrossRefGoogle Scholar
  4. 4.
    Borgatti, S.P., Everett, M.G.: Notions of position in social network analysis. Sociol. Methodol. 22, 1–35 (1992).  https://doi.org/10.2307/270991CrossRefGoogle Scholar
  5. 5.
    Borgatti, S.P., Everett, M.G.: Models of core/periphery structures. Soc. Netw. 21(4), 375–395 (1999).  https://doi.org/10.1016/S0378-8733(99)00019-2CrossRefGoogle Scholar
  6. 6.
    Borgatti, S.P., Everett, M.G.: A graph-theoretic perspective on centrality. Soc. Netw. 28(4), 466–484 (2006).  https://doi.org/10.1016/j.socnet.2005.11.005CrossRefGoogle Scholar
  7. 7.
    Borgatti, S.P., Everett, M.G., Johnson, J.C.: Analyzing Social Networks. Sage, Thousand Oaks (2013)Google Scholar
  8. 8.
    Brandes, U.: Network positions. Methodol. Innov. 9, 1–19 (2016).  https://doi.org/10.1177/2059799116630650CrossRefGoogle Scholar
  9. 9.
    Brandes, U., Borgatti, S.P., Freeman, L.C.: Maintaining the duality of closeness and betweenness centrality. Soc. Netw. 44, 153–159 (2016).  https://doi.org/10.1016/j.socnet.2015.08.003CrossRefGoogle Scholar
  10. 10.
    Brandes, U., Fleischer, D.: Centrality measures based on current flow. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 533–544. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-31856-9_44CrossRefGoogle Scholar
  11. 11.
    Brandes, U., Heine, M., Müller, J., Ortmann, M.: Positional dominance: concepts and algorithms. In: Gaur, D., Narayanaswamy, N.S. (eds.) CALDAM 2017. LNCS, vol. 10156, pp. 60–71. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-53007-9_6CrossRefzbMATHGoogle Scholar
  12. 12.
    Brandes, U., Robins, G., McCranie, A., Wasserman, S.: What is network science? Netw. Sci. 1(1), 1–15 (2013).  https://doi.org/10.1017/nws.2013.2CrossRefGoogle Scholar
  13. 13.
    Burt, R.S.: Positions in networks. Soc. Forces 55, 93–122 (1976)CrossRefGoogle Scholar
  14. 14.
    Doreian, P., Batagelj, V., Ferligoj, A.: Positional analysis of sociometric data. In: Carrington, P.J., Scott, J., Wasserman, S. (eds.) Models and Methods in Social Network Analysis, pp. 77–97. Cambridge University Press (2005)Google Scholar
  15. 15.
    Drange, P.G., Dregi, M.S., Lokshtanov, D., Sullivan, B.D.: On the threshold of intractability. In: Bansal, N., Finocchi, I. (eds.) ESA 2015. LNCS, vol. 9294, pp. 411–423. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48350-3_35CrossRefGoogle Scholar
  16. 16.
    Faust, K.: Comparison of methods for positional analysis: structural and general equivalences. Soc. Netw. 10(4), 313–341 (1988)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Freeman, L.C.: Centrality in social networks: conceptual clarification. Soc. Netw. 1(3), 215–239 (1979)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Freeman, L.C.: The development of social network analysis-with an emphasis on recent events. In: The SAGE Handbook of Social Network Analysis, pp. 26–54 (2011)Google Scholar
  19. 19.
    van der Grinten, A., Angriman, E., Meyerhenke, H.: Scaling up network centrality computations: a brief overview. it - Information Technology (2020).  https://doi.org/10.1515/itit-2019-0032
  20. 20.
    Habib, M., Medina, R., Nourine, L., Steiner, G.: Efficient algorithms on distributive lattices. Discrete Appl. Math. 110(2), 169–187 (2001).  https://doi.org/10.1016/S0166-218X(00)00258-4MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Hamilton, W.L., Ying, R., Leskovec, J.: Representation learning on graphs: methods and applications. Bull. IEEE Comput. Soc. Tech. Committee Data Eng. 40(3), 52–74 (2017)Google Scholar
  22. 22.
    Hennig, M., Brandes, U., Pfeffer, J., Mergel, I.: Studying Social Networks - A Guide to Empirical Research. Campus, Frankfurt/New York (2012)Google Scholar
  23. 23.
    Kostreva, M.M., Ogryczak, W., Wierzbicki, A.: Equitable aggregations and multiple criteria analysis. Eur. J. Oper. Res. 158(2), 362–377 (2004).  https://doi.org/10.1016/j.ejor.2003.06.010MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Lü, L., Chen, D., Ren, X.L., Zhang, Q.M., Zhang, Y.C., Zhou, T.: Vital nodes identification in complex networks. Phys. Rep. 650, 1–6 (2016)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Mariani, M.S., Ren, Z.M., Bascompte, J., Tessone, C.J.: Nestedness in complex networks: observation, emergence, and implications. Phys. Rep. 813, 1–90 (2019).  https://doi.org/10.1016/j.physrep.2019.04.001MathSciNetCrossRefGoogle Scholar
  26. 26.
    Menczer, F., Fortunato, S., Davis, C.A.: A First Course in Network Science. Cambridge University Press, Cambridge (2020)Google Scholar
  27. 27.
    Ortmann, M., Brandes, U.: Efficient orbit-aware triad and quad census in directed and undirected graphs. Appl. Netw. Sci. 2(1), 1–17 (2017).  https://doi.org/10.1007/s41109-017-0027-2CrossRefGoogle Scholar
  28. 28.
    Padgett, J.F., Ansell, C.K.: Robust action and the rise of the Medici, 1400–1434. Am. J. Sociol. 98(6), 1259–1319 (1993) CrossRefGoogle Scholar
  29. 29.
    Robins, G.: Doing Social Network Research. Sage, Thousand Oaks (2015)Google Scholar
  30. 30.
    Sabidussi, G.: The centrality index of a graph. Psychometrika 31(4), 581–603 (1966).  https://doi.org/10.1007/BF02289527MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Schoch, D.: Centrality without indices: partial rankings and rank probabilities in networks. Soc. Netw. 54, 50–60 (2018).  https://doi.org/10.1016/j.socnet.2017.12.003CrossRefGoogle Scholar
  32. 32.
    Schoch, D., Brandes, U.: Re-conceptualizing centrality in social networks. Eur. J. Appl. Math. 27(6), 971–985 (2016).  https://doi.org/10.1017/S0956792516000401MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Sommer, C.: Shortest-path queries in static networks. ACM Comput. Surv. 46(4), 45:1–45:31 (2014).  https://doi.org/10.1145/2530531
  34. 34.
    Wasserman, S., Faust, K.: Social Network Analysis. Methods and Applications. Cambridge University Press, Cambridge (1994)CrossRefGoogle Scholar
  35. 35.
    White, H.C., Boorman, S.A., Breiger, R.L.: Social structure from multiple networks: I. Blockmodels of roles and positions. Am. J. Sociol. 81(4), 730–780 (1976)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Social Networks LabETH ZürichZürichSwitzerland

Personalised recommendations