Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T16:18:03.342Z Has data issue: false hasContentIssue false
  • English
  • Français

Homophily, influence and the decay of segregation in self-organizing networks

Published online by Cambridge University Press:  23 March 2016

ADAM DOUGLAS HENRY ,
DIETER MITSCHE  and
PAWEŁ PRAŁAT
ADAM DOUGLAS HENRY
Affiliation:
School of Government and Public Policy, University of Arizona, Tucson, AZ, USA (e-mail: adhenry@email.arizona.edu)
DIETER MITSCHE
Affiliation:
Université de Nice Sophia-Antipolis, Laboratoire J-A Dieudonné, Parc Valrose, 06108 Nice cedex 02, France (e-mail: dmitsche@unice.fr)
PAWEŁ PRAŁAT
Affiliation:
Department of Mathematics, Ryerson University, Toronto, ON, Canada (e-mail: pralat@ryerson.ca)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the persistence of network segregation in networks characterized by the co-evolution of vertex attributes and link structures, in particular where individual vertices form linkages on the basis of similarity with other network vertices (homophily), and where vertex attributes diffuse across linkages, making connected vertices more similar over time (influence). A general mathematical model of these processes is used to examine the relative influence of homophily and influence in the maintenance and decay of network segregation in self-organizing networks. While prior work has shown that homophily is capable of producing strong network segregation when attributes are fixed, we show that adding even minute levels of influence is sufficient to overcome the tendency towards segregation even in the presence of relatively strong homophily processes. This result is proven mathematically for all large networks and illustrated through a series of computational simulations that account for additional network evolution processes. This research contributes to a better theoretical understanding of the conditions under which network segregation and related phenomenon—such as community structure—may emerge, which has implications for the design of interventions that may promote more efficient network structures.

Keywords

network dynamicsnetwork segregationcommunity structurehomophilyinfluencegraph theorydifferential equation methodagent-based models
Type
Research Article
Information
Network Science , Volume 4 , Issue 1 , March 2016 , pp. 81 - 116
Copyright
Copyright © Cambridge University Press 2016 

References

Aiello, W., Bonato, A., Cooper, C., Janssen, J., & Prałat, P. (2009). A spatial web graph model with local influence regions. Internet Mathematics, 5 (1), 175–196.Google Scholar
Aral, S., Muchnik, L., & Sundararajan, A. (2013). Engineering social contagions: Optimal network seeding in the presence of homophily. Network Science, 1 (2), 125–153.CrossRefGoogle Scholar
Banerjee, A., Chandrasekhar, A. G., Duflo, E., & Jackson, M. O. (2013). The diffusion of microfinance. Science, 341 (6144), 1236498.Google Scholar
Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286 (5439), 509–512.Google Scholar
Boardman, J. D., Domingue, B. W., & Fletcher, J. M. (2012). How social and genetic factors predict friendship networks. Proceedings of the National Academy of Sciences, 109 (43), 17377–17381.Google Scholar
Boucher, V. (2015). Structural homophily. International Economic Review, 56 (1), 235–264.Google Scholar
Bramoullé, Y., Currarini, S., Jackson, M. O., Pin, P., & Rogers, B. W. (2012). Homophily and long-run integration in social networks. Journal of Economic Theory, 147 (5), 1754–1786.Google Scholar
Burt, R. S. (2004). Structural holes and good ideas. American Journal of Sociology, 110 (2), 349–399.Google Scholar
Butts, C. T. (2012). sna: Tools for social network analysis. R package version 2.2-0. Retrieved from http://CRAN.R-project.org/package=sna.Google Scholar
Centola, D. (2011). An experimental study of homophily in the adoption of health behavior. Science, 334 (6060), 1269–1272.Google Scholar
Centola, D., Gonzalez-Avella, J. C., Eguiluz, V. M., & San Miguel, M. (2007). Homophily, cultural drift, & the co-evolution of cultural groups. Journal of Conflict Resolution, 51 (6), 905–929.Google Scholar
Cooper, C., Frieze, A., & Prałat, P. (2014). Some typical properties of the spatial preferred attachment model. Internet Mathematics, 10 (1–2), 27–47.Google Scholar
Cooper, C., & Prałat, P. (2011). Scale-free graphs of increasing degree. Random Structures and Algorithms, 38 (4), 396–421.Google Scholar
Currarini, S., Jackson, M. O., & Pin, P. (2009). An economic model of friendship: Homophily, minorities and segregation. Econometrica, 77 (4), 1003–1045. Retrieved from http://doi.org/10.2139/ssrn.1021650Google Scholar
Currarini, S., Jackson, M. O., & Pin, P. (2010). Identifying the roles of race-based choice and chance in high school friendship network formation. Proceedings of the National Academy of Sciences, 107 (11), 4857–4861.CrossRefGoogle Scholar
Danchin, E., Giraldeau, L.-A., Valone, T. J., & Wagner, R. H. (2004). Public information: From nosy neighbors to cultural evolution. Science, 305 (5683), 487–491.Google Scholar
Dandekar, P., Goel, A., & Lee, D. T. (2013). Biased assimilation, homophily, & the dynamics of polarization. Proceedings of the National Academy of Sciences, 110 (15), 5791–5796.CrossRefGoogle Scholar
DeGroot, M. H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69 (345), 118–121.Google Scholar
Dietz, T. (2013). Bringing values and deliberation to science communication. Proceedings of the National Academy of Sciences, 110 (Suppl 3), 14081–14087.Google Scholar
D'Souza, R. M., Borgs, C., Chayes, J. T., Berger, N., & Kleinberg, R. D. (2007). Emergence of tempered preferential attachment from optimization. Proceedings of the National Academy of Sciences, 104 (15), 6112–6117.Google Scholar
Durrett, R.et al. (2012). Graph fission in an evolving voter model. Proceedings of the National Academy of Sciences, 109 (10), 3682–3687.CrossRefGoogle Scholar
Freeman, L. C. (1978). Segregation in social networks. Sociological Methods & Research, 6 (4), 411–429.Google Scholar
Friedkin, N. E., & Johnsen, E. C. (2011). Social influence network theory: A sociological examination of small group dynamics. Cambridge: Cambridge University Press.Google Scholar
Gerber, E. R., Henry, A. D., & Lubell, M. (2013). Political homophily and collaboration in regional planning networks. American Journal of Political Science, 57 (3), 598–610.Google Scholar
Girard, Y., Hett, F., & Schunk, D. (2015). How individual characteristics shape the structure of social networks. Journal of Economic Behavior & Organization, 115, 197–216.Google Scholar
Girvan, M., & Newman, M. E. J. (2002). Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99 (12), 7821–7826.Google Scholar
Golub, B., & Jackson, M. O. (2012). Does homophily predict consensus times? Testing a model of network structure via a dynamic process. Review of Network Economics, 11 (3), 9.Google Scholar
Granovetter, M. S. (1973). The strength of weak ties. The American Journal of Sociology, 78 (6), 1360–1380.Google Scholar
Harris, K. M., Halpern, C. T., Whitsel, E., Hussey, J., Tabor, J., Entzel, P., & Udry, J. R. (2009). The national longitudinal study of adolescent to adult health: Research design. Retrieved from http://www.cpc.unc.edu/projects/addhealth/design.Google Scholar
Henry, A. D. (2009). The challenge of learning for sustainability: A prolegomenon to theory. Human Ecology Review, 16 (2), 131–140.Google Scholar
Henry, A. D. (2011). Ideology, power, & the structure of policy networks. Policy Studies Journal, 39 (3), 361–383.Google Scholar
Henry, A. D., Lubell, M., & McCoy, M. (2011a). Belief systems and social capital as drivers of policy network structure: The case of California regional planning. Journal of Public Administration Research and Theory, 21 (3), 419–444.Google Scholar
Henry, A. D., & Prałat, P. (2013). Discovery of nodal attributes through a rank-based model of network structure. Internet Mathematics, 9 (1), 33–57.Google Scholar
Henry, A. D., Prałat, P., & Zhang, C.-Q. (2011b). Emergence of segregation in evolving social networks. Proceedings of the National Academy of Sciences, 108 (21), 8605–8610.CrossRefGoogle Scholar
Hong, L., & Page, S. E. (2004). Groups of diverse problem solvers can outperform groups of high-ability problem solvers. Proceedings of the National Academy of Sciences, 101 (46), 16385–16389.Google Scholar
Jackson, M. O. (2014). Networks in the understanding of economic behaviors. Journal of Economic Perspectives, 28 (4), 3–22.CrossRefGoogle Scholar
Jackson, M. O., & López-Pintado, D. (2013). Diffusion and contagion in networks with heterogeneous agents and homophily. Network Science, 1 (1), 49–67.CrossRefGoogle Scholar
Janson, S., łuczak, T., & Ruciński, A. (2000). Random graphs. New York: Wiley.CrossRefGoogle Scholar
Kleinbaum, A. M., Stuart, T. E., & Tushman, M. L. (2013). Discretion within constraint: Homophily and structure in a formal organization. Organization Science, 24 (5), 1316–1336.Google Scholar
Kossinets, G., & Watts, D. J. (2009). Origins of homophily in an evolving social network. American Journal of Sociology, 115 (2), 405–450.Google Scholar
Krause, A. E., Frank, K. A., Mason, D. M., Ulanowicz, R. E., & Taylor, W. W. (2003). Compartments revealed in food-web structure. Nature, 426 (6964), 282–285.Google Scholar
Kumpula, J., Onnela, J.-P., Saramäki, J., Kaski, K., & Kertész, J. (2007). Emergence of communities in weighted networks. Physical Review Letters, 99 (22), 228701.CrossRefGoogle Scholar
Lambiotte, R., Ausloos, M., & Holyst, J. (2007). Majority model on a network with communities. Physical Review E, 75 (3), R030101.Google Scholar
Lazer, D. (2001). The co-evolution of individual and network. The Journal of Mathematical Sociology, 25 (1), 69–108.Google Scholar
Lewis, K., Gonzalez, M., & Kaufman, J. (2012). Social selection and peer influence in an online social network. Proceedings of the National Academy of Sciences, 109 (1), 68–72.Google Scholar
McPherson, M., Smith-Lovin, L., & Cook, J. M. (2001). Birds of a feather: Homophily in social networks. Annual Review of Sociology, 27, 415–444.Google Scholar
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45 (2), 167–256.CrossRefGoogle Scholar
Newman, M. E. J. (2006). Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103 (23), 8577–8582.Google Scholar
Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314 (5805), 1560–1563.Google Scholar
Palla, G., Barabási, A.-L., & Vicsek, T. (2007). Quantifying social group evolution. Nature, 446 (7136), 664–667.Google Scholar
Palla, G., Derényi, I., Farkas, I., & Vicsek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435 (7043), 814–818.Google Scholar
Parson, E. A., & Clark, W. C. (2005). Barriers and bridges to the renewal of ecosystems and institutions (pp. 428–460). New York: Columbia University Press.Google Scholar
Porter, M. A., Onnela, J.-P., & Mucha, P. J. (2009). Communities in Networks. Notices of the American Mathematical Society, 56 (9), 1082–1097.Google Scholar
R Core Team (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, Retreived from http://www.R-project.org/.Google Scholar
Sabatier, P. E. (2007). Theories of the policy process. Boulder, CO: Westview Press.Google Scholar
Sabatier, P. E., & Jenkins-Smith, H. C. (1993). Policy change and learning: An advocacy coalition approach. Boulder, CO: Westview Press.Google Scholar
Valente, T. W. (1995). Network models of the diffusion of innovations. Cresskill, NJ: Hampton Press.Google Scholar
Wormald, N. (1999). The differential equation method for random graph processes and greedy algorithms. In Karoński, M., & Prömel, H. J. (Eds.), Lectures on approximation and randomized algorithms (pp. 73–155). Warsaw: PWN.Google Scholar