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Friendship Formation in the Classroom Among Elementary School Students

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Complex Networks and Their Applications VIII (COMPLEX NETWORKS 2019)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 882))

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Abstract

We used Exponential Random Graph Models (ERGMs) to determine how important is the role played by homophily, transitivity and preferential attachment effects in the formation of friendship networks obtained from data collected in 3 elementary schools; two are located in the rural area and the other is in the urban area of Yucatán, México. Structural terms were considered, as well as individual attributes (gender and scholar grade) of each student in the network. We hypothesize three network effects thought to contribute to the observed structure: homophily, triad closure and preferential attachment. Assessment model was done using p-value, Akaike information criteria (AIC) and a graphical goodness of fit (GOF). Results from exponential random graph models support our hypothesized homophily and triad closure effects. All friendship networks in our investigation had positive and significant triad closure and homophily effects. On the other hand, we do not find evidence for preferential attachment processes. Well connected students are not more prone to gain additional links than sparsely connected students.

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References

  1. Huerta-Quintanilla, R., Canto-Lugo, E., Viga-de Alva, D.: Modeling social network topologies in elementary schools. PLoS ONE 8(2), e55371 (2013)

    Article  Google Scholar 

  2. Goodreau, S.M., Kitts, J.A., Morris, M.: Birds of a feather, or friend of a friend? Using exponential random graph models to investigate adolescent social networks. Demography 46(1), 103–125 (2009)

    Article  Google Scholar 

  3. Flores, M.A.R., Papadopoulos, F.: Similarity forces and recurrent components in human face-to-face interaction networks. Phys. Rev. Lett. 121(25), 258301 (2018)

    Article  Google Scholar 

  4. Isella, L., Stehlé, J., Barrat, A., Cattuto, C., Pinton, J.F., Van den Broeck, W.: What’s in a crowd? Analysis of face-to-face behavioral networks. J. Theor. Biol. 271(1), 166–180 (2011)

    Article  MathSciNet  Google Scholar 

  5. Baerveldt, C., Van de Bunt, G.G., Vermande, M.M.: Selection patterns, gender and friendship aim in classroom networks. Zeitschrift für Erziehungswissenschaft. 17(5), 171–188 (2014)

    Article  Google Scholar 

  6. Oldenburg, B., Van Duijn, M., Veenstra, R.: Defending one’s friends, not one’s enemies: a social network analysis of children’s defending, friendship, and dislike relationships using XPNet. PLoS ONE 13(5), e0194323 (2018)

    Article  Google Scholar 

  7. Jiao, C., Wang, T., Liu, J., Wu, H., Cui, F., Peng, X.: Using Exponential Random Graph Models to analyze the character of peer relationship networks and their effects on the subjective well-being of adolescents. Front. Psychol. 8, 583 (2017)

    Article  Google Scholar 

  8. Wax, A., DeChurch, L.A., Contractor, N.S.: Self-organizing into winning teams: understanding the mechanisms that drive successful collaborations. Small Group Res. 48(6), 665–718 (2017)

    Article  Google Scholar 

  9. Jeong, H., Néda, Z., Barabási, A.L.: Measuring preferential attachment in evolving networks. EPL (Europhys. Lett.) 61(4), 567 (2003)

    Article  Google Scholar 

  10. Newman, M.E.: Clustering and preferential attachment in growing networks. Phys. Rev. E 64(2), 025102 (2001)

    Article  Google Scholar 

  11. Bianconi, G., Darst, R.K., Iacovacci, J., Fortunato, S.: Triadic closure as a basic generating mechanism of communities in complex networks. Phys. Rev. E 90(4), 042806 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Conway, D.: Modeling network evolution using graph motifs. arXiv preprint arXiv:11050902 (2011)

  14. Desmarais, B.A., Cranmer, S.J.: Statistical mechanics of networks: estimation and uncertainty. Phys. A 391(4), 1865–1876 (2012)

    Article  Google Scholar 

  15. Saul, Z.M., Filkov, V.: Exploring biological network structure using exponential random graph models. Bioinformatics 23(19), 2604–2611 (2007)

    Article  Google Scholar 

  16. Yletyinen, J., Bodin, Ö., Weigel, B., Nordström, M.C., Bonsdorff, E., Blenckner, T.: Regime shifts in marine communities: a complex systems perspective on food web dynamics. Proc. Roy. Soc. B Biol. Sci. 2016(283), 20152569 (1825)

    Google Scholar 

  17. Yang, D.H., Yu, G.: Static analysis and exponential random graph modelling for micro-blog network. J. Inf. Sci. 40(1), 3–14 (2014)

    Article  Google Scholar 

  18. Krivitsky, P.N.: Using contrastive divergence to seed Monte Carlo MLE for exponential-family random graph models. Comput. Stat. Data Anal. 107, 149–161 (2017)

    Article  MathSciNet  Google Scholar 

  19. Alexandridis, G., Siolas, G., Stafylopatis, A.: Enhancing social collaborative filtering through the application of non-negative matrix factorization and exponential random graph models. Data Min. Knowl. Disc. 31(4), 1031–1059 (2017)

    Article  MathSciNet  Google Scholar 

  20. Kukielka, E.A., Martínez-López, B., Beltrán-Alcrudo, D.: Modeling the live-pig trade network in Georgia: implications for disease prevention and control. PLoS ONE 12(6), e0178904 (2017)

    Article  Google Scholar 

  21. Hermans, F., Sartas, M., Van Schagen, B., van Asten, P., Schut, M.: Social network analysis of multi-stakeholder platforms in agricultural research for development: opportunities and constraints for innovation and scaling. PLoS ONE 12(2), e0169634 (2017)

    Article  Google Scholar 

  22. Nita, A., Rozylowicz, L., Manolache, S., Ciocănea, C.M., Miu, I.V., Popescu, V.D.: Collaboration networks in applied conservation projects across Europe. PLoS ONE 11(10), e0164503 (2016)

    Article  Google Scholar 

  23. De La Haye, K., Dijkstra, J.K., Lubbers, M.J., Van Rijsewijk, L., Stolk, R.: The dual role of friendship and antipathy relations in the marginalization of overweight children in their peer networks: the TRAILS Study. PLoS ONE 12(6), e0178130 (2017)

    Article  Google Scholar 

  24. Cherepnalkoski, D., Karpf, A., Mozetič, I., Grčar, M.: Cohesion and coalition formation in the European Parliament: roll-call votes and Twitter activities. PLoS ONE 11(11), e0166586 (2016)

    Article  Google Scholar 

  25. Salehi, S., Holmes, N., Wieman, C.: Exploring bias in mechanical engineering students’ perceptions of classmates. PLoS ONE 14(3), e0212477 (2019)

    Article  Google Scholar 

  26. Campbell, B.W., Marrs, F.W., Böhmelt, T., Fosdick, B.K., Cranmer, S.J.: Latent influence networks in global environmental politics. PLoS ONE 14(3), e0213284 (2019)

    Article  Google Scholar 

  27. Newman, M.: Networks. Oxford University Press, Oxford (2018)

    Book  Google Scholar 

  28. Dietterich, T.G.: Ensemble methods in machine learning. In: International Workshop on Multiple Classifier Systems, pp. 1–15. Springer (2000)

    Google Scholar 

  29. Park, J., Newman, M.E.: Solution of the two-star model of a network. Phys. Rev. E 70(6), 066146 (2004)

    Article  MathSciNet  Google Scholar 

  30. Park, J., Newman, M.: Solution for the properties of a clustered network. Phys. Rev. E 72(2), 026136 (2005)

    Article  Google Scholar 

  31. Snijders, T.A., Pattison, P.E., Robins, G.L., Handcock, M.S.: New specifications for exponential random graph models. Sociol. Methodol. 36(1), 99–153 (2006)

    Article  Google Scholar 

  32. Hunter, D.R., Handcock, M.S.: Inference in curved exponential family models for networks. J. Comput. Graph. Stat. 15(3), 565–583 (2006)

    Article  MathSciNet  Google Scholar 

  33. Angst, M., Hirschi, C.: Network dynamics in natural resource governance: a case study of Swiss landscape management. Policy Stud. J. 45(2), 315–336 (2017)

    Article  Google Scholar 

  34. Levy, M.A., Lubell, M.N.: Innovation, cooperation, and the structure of three regional sustainable agriculture networks in California. Reg. Environ. Change 18(4), 1235–1246 (2018)

    Article  Google Scholar 

  35. Hunter, D.R., Handcock, M.S., Butts, C.T., Goodreau, S.M., Morris, M.: ergm: A package to fit, simulate and diagnose exponential-family models for networks. J. Stat. Softw. 24(3), nihpa54860 (2008)

    Article  Google Scholar 

  36. Handcock, M.S., Hunter, D.R., Butts, C.T., Goodreau, S.M., Morris, M.: statnet: Software tools for the representation, visualization, analysis and simulation of network data. J. Stat. Softw. 24(1), 1548 (2008)

    Article  Google Scholar 

  37. Stehlé, J., Charbonnier, F., Picard, T., Cattuto, C., Barrat, A.: Gender homophily from spatial behavior in a primary school: a sociometric study. Soc. Netw. 35(4), 604–613 (2013)

    Article  Google Scholar 

  38. Hernández-Hernández, A.M., Viga-de Alva, D., Huerta-Quintanilla, R., Canto-Lugo, E., Laviada-Molina, H., Molina-Segui, F.: Friendship concept and community network structure among elementary school and university students. PLoS ONE 11(10), e0164886 (2016)

    Article  Google Scholar 

  39. Rombach, M.P., Porter, M.A., Fowler, J.H., Mucha, P.J.: Core-periphery structure in networks. SIAM J. Appl. Math. 74(1), 167–190 (2014)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Departamento de Física Aplicada, Centro de investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Mérida, Yucatán, Mexico

    Raúl Duarte-Barahona, Ezequiel Arceo-May & Rodrigo Huerta-Quintanilla

Authors
  1. Raúl Duarte-Barahona
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  2. Ezequiel Arceo-May
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  3. Rodrigo Huerta-Quintanilla
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Corresponding author

Correspondence to Raúl Duarte-Barahona .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  2. Università degli Studi di Milano, Milan, Italy

    Sabrina Gaito

  3. University of Aveiro, Aveiro, Portugal

    José Fernendo Mendes

  4. Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

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Duarte-Barahona, R., Arceo-May, E., Huerta-Quintanilla, R. (2020). Friendship Formation in the Classroom Among Elementary School Students. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 882. Springer, Cham. https://doi.org/10.1007/978-3-030-36683-4_33

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