Symmetric core-cohesive blockmodel in preschool children’s interaction networks


Autoři: Marjan Cugmas aff001;  Dawn DeLay aff002;  Aleš Žiberna aff001;  Anuška Ferligoj aff001
Působiště autorů: Centre for Methodology and Informatics, Faculty of Social Sciences, University of Ljubljana, Ljubljana, Slovenia aff001;  Sanford School of Social and Family Dynamics, Arizona State University, Tempe, Arizona, United States of America aff002;  International Laboratory for Applied Network Research, National Research University Higher School of Economics, Moscow, Russia aff003
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article
doi: 10.1371/journal.pone.0226801

Souhrn

Researchers have extensively studied the social mechanisms that drive the formation of networks observed among preschool children. However, less attention has been given to global network structures in terms of blockmodels. A blockmodel is a network where the nodes are groups of equivalent units (according to links to others) from a studied network. It is already shown that mutuality, popularity, assortativity, and different types of transitivity mechanisms can lead the global network structure to the proposed asymmetric core-cohesive blockmodel. Yet, they did not provide any evidence that such a global network structure actually appears in any empirical data. In this paper, the symmetric version of the core-cohesive blockmodel type is proposed. This blockmodel type consists of three or more groups of units. The units from each group are internally well linked to each other while those from different groups are not linked to each other. This is true for all groups, except one in which the units have mutual links to all other units in the network. In this study, it is shown that the proposed blockmodel type appears in empirical interactional networks collected among preschool children. Monte Carlo simulations confirm that the most often studied social network mechanisms can lead the global network structure to the proposed symmetric blockmodel type. The units’ attributes are not considered in this study.

Klíčová slova:

Algorithms – Children – Monte Carlo method – Network analysis – Network reciprocity – Schools – Simulation and modeling – Social networks


Zdroje

1. Bianconi G, Darst RK, Iacovacci J, Fortunato S. Triadic closure as a basic generating mechanism of communities in complex networks. Physical Review E. 2014;90(4):042806. doi: 10.1103/PhysRevE.90.042806

2. Cugmas M, Žiberna A, Ferligoj A. Mechanisms generating asymmetric core-cohesive blockmodels. Metodološki zvezki. 2019;16(1):17–41.

3. Fabes RA, Martin CL, Hanish LD. The next 50 years: Considering gender as a context for understanding young children’s peer relationships. Merrill-Palmer Quarterly. 2004;50(3):260–273. doi: 10.1353/mpq.2004.0017

4. Martin CL, Fabes RA, Hanish LD, Hollenstein T. Social dynamics in the preschool. Developmental Review. 2005;25(3-4):299–327. doi: 10.1016/j.dr.2005.10.001

5. Doreian P, Batagelj V, Ferligoj A. Generalized blockmodeling. Cambridge: Cambridge University Press; 2005.

6. Schaefer DR, Light JM, Fabes RA, Hanish LD, Martin CL. Fundamental principles of network formation among preschool children. Social networks. 2010;32(1):61–71. doi: 10.1016/j.socnet.2009.04.003 20161606

7. Brown BB, Klute C. Friendships, cliques, and crowds. In: Adams G, Berzonsky M, editors. Blackwell Handbook of Adolescence. Wiley-Blackwell; 2003. p. 266–290.

8. Lorrain F, White H. Structural equivalence of individuals in social networks. The Journal of Mathematical Sociology. 1971;1(1):49–80. doi: 10.1080/0022250X.1971.9989788

9. Batagelj V, Ferligoj A, Doreian P. Direct and indirect methods for structural equivalence. Social Networks. 1992;14(1-2):63–90. doi: 10.1016/0378-8733(92)90014-X

10. White DR, Reitz KP. Graph and semigroup homomorphisms on networks of relations. Social Networks. 1983;5(2):193–234. doi: 10.1016/0378-8733(83)90025-4

11. Stadtfeld C, Takács K, Vörös A. The Emergence and Stability of Groups in Social Networks. SSRN. 2018; p. 1–60.

12. Maccoby EE, Jacklin CN. Gender segregation in childhood. In: Advances in child development and behavior. Elsevier; 1987. p. 239–287.

13. Vaughn BE, Colvin TN, Azria MR, Caya L, Krzysik L. Dyadic analyses of friendship in a sample of preschool-age children attending Head Start: Correspondence between measures and implications for social competence. Child development. 2001;72(3):862–878. doi: 10.1111/1467-8624.00320 11405587

14. Daniel JR, Santos AJ, Peceguina I, Vaughn BE. Exponential random graph models of preschool affiliative networks. Social Networks. 2013;35(1):25–30. doi: 10.1016/j.socnet.2012.11.002

15. Snyder J, West L, Stockemer V, Gibbons S, Almquist-Parks L. A social learning model of peer choice in the natural environment. Journal of Applied Developmental Psychology. 1996;17(2):215–237. doi: 10.1016/S0193-3973(96)90026-X

16. Block P. Reciprocity, transitivity, and the mysterious three-cycle. Social Networks. 2015;40:163–173. doi: 10.1016/j.socnet.2014.10.005

17. Kandel DB. Homophily, selection, and socialization in adolescent friendships. American journal of Sociology. 1978;84(2):427–436. doi: 10.1086/226792

18. McPherson M, Smith-Lovin L, Cook JM. Birds of a feather: Homophily in social networks. Annual review of sociology. 2001;27:415–444. doi: 10.1146/annurev.soc.27.1.415

19. Dijkstra JK, Cillessen AH, Borch C. Popularity and adolescent friendship networks: Selection and influence dynamics. Developmental Psychology. 2013;49(7):1242–1252. doi: 10.1037/a0030098 22985296

20. Cillessen AH, Rose AJ. Understanding popularity in the peer system. Current Directions in Psychological Science. 2005;14(2):102–105. doi: 10.1111/j.0963-7214.2005.00343.x

21. Robins G, Pattison P, Kalish Y, Lusher D. An introduction to exponential random graph (p*) models for social networks. Social networks. 2007;29(2):173–191.

22. Block P, Stadtfeld C, Snijders TA. Forms of Dependence Comparing SAOMs and ERGMs From Basic Principles. Sociological Methods & Research. 2019;48(1):202–239. doi: 10.1177/0049124116672680

23. Handcock MS, Robins G, Snijders T, Moody J, Besag J. Assessing Degeneracy in Statistical Models of Social Networks. Journal of the American Statistical Association. 2003;76:33–50.

24. Snijders TA, Van de Bunt GG, Steglich CE. Introduction to stochastic actor-based models for network dynamics. Social networks. 2010;32(1):44–60. doi: 10.1016/j.socnet.2009.02.004

25. Hartup WW, Stevens N. Friendships and adaptation in the life course. Psychological bulletin. 1997;121(3):355–370. doi: 10.1037/0033-2909.121.3.355

26. Hartup WW. Adolescents and their friends. New Directions for Child and Adolescent Development. 1993;1993(60):3–22. doi: 10.1002/cd.23219936003

27. Žiberna A. Generalized and Classical Blockmodeling of Valued Networks; 2018. Available from: https://cran.r-project.org/web/packages/blockmodeling/blockmodeling.pdf.

28. Van de Bunt GG, Groenewegen P. An Actor-Oriented Dynamic Network Approach: The Case of Interorganizational Network Evolution Organizational Research Methods. 2007;10(3):463–482. doi: 10.1177/1094428107300203

29. Bauer F, Hansen T, Hellsmark H. Innovation in the bioeconomy—dynamics of biorefinery innovation networks Technology Analysis & Strategic Managment. 2018;30(8):935–947. doi: 10.1080/09537325.2018.1425386

30. Snijders T. Stochastic Actor-Oriented Models for Network Dynamics Annual Review of Statistics and Its Application. 2017;4(1):434–363. doi: 10.1146/annurev-statistics-060116-054035

31. Toivonen R, Kovanen L, Kivelä M, Onnela JP, Saramäki J, Kaski K. A comparative study of social network models: Network evolution models and nodal attribute models. Social Networks. 2009;31(4):240–254. doi: 10.1016/j.socnet.2009.06.004

32. Robins G, Pattison P, Wang P. Closure, connectivity and degree distributions: Exponential random graph (p*) models for directed social networks. Social Networks. 2009;31(2):105–117. doi: 10.1016/j.socnet.2008.10.006

33. Marsaglia G. Choosing a point from the surface of a sphere. The Annals of Mathematical Statistics. 1972;43(2):645–646. doi: 10.1214/aoms/1177692644

34. Muller ME. A note on a method for generating points uniformly on n-dimensional spheres. Communications of the ACM. 1959;2(4):19–20. doi: 10.1145/377939.377946

35. Batagelj V. Notes on blockmodeling. Social Networks. 1997;19(2):143–155. doi: 10.1016/S0378-8733(96)00297-3

36. Doreian P, Batagelj V, Ferligoj A. Partitioning networks based on generalized concepts of equivalence. Journal of Mathematical Sociology. 1994;19(1):1–27. doi: 10.1080/0022250X.1994.9990133


Článek vyšel v časopise

PLOS One


2020 Číslo 1