Skip to main content
Log in

Micro- and macromodels of social networks. I. Theory fundamentals

  • Control Sciences
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We consider two approaches to the design and analysis of social networks, namely, macro- and microdescriptions. According to the former approach, the structure of relations in a social network is averaged, and agents’ behavior is studied “in the mean.” The latter approach takes into account the structural features of the influence graph of agents and their individual decision-making principles. The first and second approaches are compared using the threshold model of collective behavior with a common relative threshold.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Barabanov, I.N., Korgin, N.A., Novikov, D.A., and Chkhartishvili, A.G., Dynamic Models of Informational Control in Social Networks, Autom. Remote Control, 2010, vol. 71, no. 11, pp. 2417–2426.

    Article  MathSciNet  MATH  Google Scholar 

  2. Batov, A.V., Breer, V.V., Novikov, D.A., and Rogatkin, A.D., Micro- and Macromodels of Social Networks. II. Identification and Simulation Experiments, Autom. Remote Control, 2016, vol. 77, no., pp. 199–209.

    Article  Google Scholar 

  3. Breer, V.V., Conformal Behavior Models. I. From Philosophy to Math Models, Probl. Upravlen., 2014, no. 1, pp. 2–13.

    Google Scholar 

  4. Breer, V.V., Conformal Behavior Models. II. Mathematical Models, Probl. Upravlen., 2014, no. 2, pp. 2–17.

    Google Scholar 

  5. Breer, V.V., Game-Theoretic Models of Collective Conformity Behavior, Autom. Remote Control, 2012, vol. 73, no. 10, pp. 1680–1692.

    Article  MathSciNet  MATH  Google Scholar 

  6. Breer, V.V. and Novikov, D.A., Models of Mob Control, Autom. Remote Control, 2013, vol. 74, no. 12, pp. 2143–2154.

    Article  MathSciNet  Google Scholar 

  7. Breer, V.V., Stochastic Models of Social Networks, Upravlen. Bol’shimi Sist., 2009, no. 27, pp. 169–204.

    Google Scholar 

  8. Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988, 4th ed. Translated into English under the title Theory of Matrices, New York: Chelsea, 1959.

    Google Scholar 

  9. Gubanov, D.A., Novikov, D.A., and Chkhartishvili, A.G., Models of Reputation and Information Control in Social Networks, Upravlen. Bol’shimi Sist., 2009, no. 26.1, pp. 209–234.

    Google Scholar 

  10. Gubanov, D.A., Novikov, D.A., and Chkhartishvili, A.G., Sotsial’nye seti: modeli informatsionnogo vliyaniya, upravleniya i protivoborstva (Social Networks: Models of Informational Influence, Control, and Contagion), Moscow: Fizmatlit, 2010.

    Google Scholar 

  11. Gubanov, D.A., A Survey of Online Reputation/Confidence Systems, Internet Conference on Control Problems, Inst. Probl. Upravlen., Moscow, 2009. URL: www.mtas.ru/forum.

    Google Scholar 

  12. Gubanov, D.A. and Chkhartishvili, A.G., An Actional Model of Influential Users in Social Networks, Autom. Remote Control, 2015, vol. 76, no. 7, pp. 1282–1290.

    Article  MathSciNet  Google Scholar 

  13. Yevin, I.A., Introduction to the Theory of Complex Networks, Komp. Issl. Modelir., 2010, vol. 2, no. 2, pp. 121–141.

    Google Scholar 

  14. Kolchin, V.F., Sluchainye grafy (Random Graphs), Moscow: Fizmatlit, 2004, 2nd ed.

    Google Scholar 

  15. Novikov, D.A., Big Data: From Brahe—To Newton, Probl. Upravlen., 2013, no. 6, pp. 15–23.

    Google Scholar 

  16. Novikov, D.A., Hierarchical Models of Warfare, Autom. Remote Control, 2013, vol. 74, no. 10, pp. 1733–1752.

    Article  MathSciNet  MATH  Google Scholar 

  17. Novikov, D.A., Models of Network Excitation Control, Tr. XII Vseross. Soveshchaniya Po Problemam Upravleniya (Proc. XII All-Russia Meeting on Control Problems), Inst. Probl. Upravlen., Moscow, 2014.

    Google Scholar 

  18. Raigorodskii, A.M., Models of Random Graphs and Their Applications, Tr. MFTI, 2010, vol. 2, no. 4, pp. 130–140.

    MathSciNet  Google Scholar 

  19. Slovokhotov, Y.L., Physics vs. Sociophysics, I–III, Probl. Upravlen., 2012, no. 1, pp. 2–20; no. 2, pp. 2–31; no. 3, pp. 2–34.

    Google Scholar 

  20. Chebotarev, P.Yu. and Agaev, R.P., Coordination in Multiagent Systems and Laplacian Spectra of Digraphs, Autom. Remote Control, 2009, vol. 70, no. 3, pp. 469–483.

    Article  MathSciNet  MATH  Google Scholar 

  21. Shiryaev, A.N., Veroyatnost’ (Probability), Moscow: Nauka, 1989.

    Google Scholar 

  22. Albert, R. and Barabasi, A.-L., Statistical Mechanics of Complex Networks, Rev. Mod. Phys., 2002, no. 74, pp. 47–97.

    Article  MathSciNet  MATH  Google Scholar 

  23. Barabasi, A. and Albert, R., Emergence of Scaling in Random Networks, Science, 1999, no. 286, pp. 509–512.

    Article  MathSciNet  Google Scholar 

  24. Barabasi, A., Scale-free Networks, Scientific Am., 2003, no. 5, pp. 50–59.

    Google Scholar 

  25. Bollobas, B., Random Graphs, Cambridge: Cambridge Univ. Press, 2001.

    Book  MATH  Google Scholar 

  26. Chen, N., On the Approximability of Influence in Social Networks, SIAM J. Discrete Math., 2009, vol. 23, pp. 1400–1415.

    Article  MathSciNet  MATH  Google Scholar 

  27. De Groot, M., Reaching a Consensus, J. Am. Statist. Ass., 1974, no. 69, pp. 118–121.

    Article  Google Scholar 

  28. Dorogovtsev, S., Lectures on Complex Networks, Oxford: Oxford Univ. Press, 2010.

    Book  MATH  Google Scholar 

  29. Dorogovtsev, S. and Mendes, J., Evolution of Networks, Oxford: Clarendon Press, 2010.

    Google Scholar 

  30. Durett, R., Random Graph Dynamics, Cambridge: Cambridge Univ. Press, 2007.

    Google Scholar 

  31. Erdos, P. and Renyi, A., On Random Graphs, Publ. Math. Debrecen, 1959, no. 6, pp. 290–297.

    MathSciNet  Google Scholar 

  32. Goldenberg, J., Libai, B., and Muller, E., Talk of the Network: A Complex Systems Look at the Underlying Process of Word-of-Mouth, Market. Lett., 2001, vol. 12, no. 3, pp. 211–223.

    Article  Google Scholar 

  33. Granovetter, M., Threshold Models of Collective Behavior, Am. J. Sociology, 1978, vol. 83, pp. 1420–1443.

    Article  Google Scholar 

  34. Kempe, D., Kleinberg, J., and Tardos, E., Maximizing the Spread of Influence through a Social Network, Proc. 9th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, Washington, 2003, 137–146.

    Google Scholar 

  35. Lin, Y., Shi, X., and Wei, Y., On Computing PageRank via Lumping the Google Matrix, J. Comput. Appl. Math., 2009, vol. 224, no. 2, pp. 702–708.

    Article  MathSciNet  MATH  Google Scholar 

  36. Newman, M., The Structure and Function of Complex Networks, SIAM Rev., 2003, vol. 45, no. 2, pp. 167–256.

    Article  MathSciNet  MATH  Google Scholar 

  37. Nemhauser, G., Wolsey, L., and Fisher, M., An Analysis of the Approximations for Maximizing Submodular Set Functions, Math. Progr., 1978, vol. 14, pp. 265–294.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. V. Breer.

Additional information

Original Russian Text © V.V. Breer, D.A. Novikov, A.D. Rogatkin, 2014, published in Problemy Upravleniya, 2014, No. 5, pp. 28–33.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Breer, V.V., Novikov, D.A. & Rogatkin, A.D. Micro- and macromodels of social networks. I. Theory fundamentals. Autom Remote Control 77, 313–320 (2016). https://doi.org/10.1134/S0005117916020077

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117916020077

Keywords

Navigation