Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-23T06:25:39.640Z Has data issue: false hasContentIssue false
  • English
  • Français

Friendship networks and social status

Published online by Cambridge University Press:  15 April 2013

BRIAN BALL  and
M.E.J. NEWMAN
BRIAN BALL
Affiliation:
Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA (e-mail: briball@umich.edu)
M.E.J. NEWMAN
Affiliation:
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA (e-mail: mejn@umich.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

In empirical studies of friendship networks, participants are typically asked, in interviews or questionnaires, to identify some or all of their close friends, resulting in a directed network in which friendships can, and often do, run in only one direction between a pair of individuals. Here we analyze a large collection of such networks representing friendships among students at US high and junior-high schools and show that the pattern of unreciprocated friendships is far from random. In every network, without exception, we find that there exists a ranking of participants, from low to high, such that almost all unreciprocated friendships consist of a lower ranked individual claiming friendship with a higher ranked one. We present a maximum-likelihood method for deducing such rankings from observed network data and conjecture that the rankings produced reflect a measure of social status. We note in particular that reciprocated and unreciprocated friendships obey different statistics, suggesting different formation processes, and that rankings are correlated with other characteristics of the participants that are traditionally associated with status, such as age and overall popularity as measured by total number of friends.

Keywords

friendship networkssocial statusmaximum likelihoodstochastic blockmodel
Type
Research Article
Information
Network Science , Volume 1 , Issue 1 , April 2013 , pp. 16 - 30
Copyright
Copyright © Cambridge University Press 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Airoldi, Edoardo M., Choi, David S., & Wolfe, Patrick J. (2011). Confidence sets for network structure. Statistical Analysis and Data Mining, 4, 461–469.Google Scholar
Ali, I., Cook, W. D., & Kress, M. (1986). On the minimum violations ranking of a tournament. Management Science, 32, 660–672.Google Scholar
Anderson, C., Srivastava, S., Beer, Jennifer S., Spataro, Sandra E., & Chatman, Jennifer A. (2006). Knowing your place: Self-perceptions of status in face-to-face groups. Journal of Personality and Social Psychology, 91, 1094–1110.CrossRefGoogle ScholarPubMed
Callaghan, T., Mucha, P. J., & Porter, M. A. (2004). The bowl championship series: A mathematical review. Notices of the American Mathematical Society, 51, 887–893.Google Scholar
Coleman, James S. (1961). The Adolescent Society: The Social Life of the Teenager and Its Impact on Education. Westport, CT: Greenwood Press.Google Scholar
Davis, James A., & Leinhardt, S. (1972). The structure of positive interpersonal relations in small groups. Sociological Theories in Progress, 2, 218–251.Google Scholar
De Vries, H. (1998). Finding a dominance order most consistent with a linear hierarchy: A new procedure and review. Animal Behaviour, 55, 827–843.Google Scholar
Dijkstra, J. K., Cillessen, Antonius H. N., Lindenberg, S., & Veenstra, R. (2010). Basking in reflected glory and its limits: Why adolescents hang out with popular peers. Journal of Research on Adolescents, 20, 942–958.Google Scholar
Doreian, P., Batagelj, V., & Ferligoj, A. (2000). Symmetric-acyclic decompositions of networks. Journal of Classification, 17, 3–28.Google Scholar
Drews, C. (1993). The concept and definition of dominance in animal behaviour. Behaviour, 125, 283–313.Google Scholar
Goldenberg, A., Zheng, Alice X., Feinberg, Stephen E., & Airoldi, Edoardo M. (2009). A survey of statistical network structures. Foundations and Trends in Machine Learning, 2, 1–117.Google Scholar
Hallinan, Maureen T., & Kubitschek, Warren N. (1988). The effect of individual and structural characteristics on intransitivity in social networks. Social Psychology Quarterly, 51, 81–92.CrossRefGoogle Scholar
Holland, P. W., & Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 76, 33–50.CrossRefGoogle Scholar
Homans, G. C. (1950). The Human Group. San Diego, CA: Harcourt Brace.Google Scholar
Karrer, B., & Newman, M. E. J. (2011). Stochastic blockmodels and community structure in networks. Physical Review E, 83, 016107.Google Scholar
Rapoport, A., & Horvath, W. J. (1961). A study of a large sociogram. Behavioral Science, 6, 279–291.Google Scholar
Reinelt, G. (1985). The Linear Ordering Problem: Algorithms and Applications. Berlin, Germany: Heldermann.Google Scholar
Snijders, Tom A. B. (2011). Statistical models for social networks. Annual Review of Sociology, 37, 131–153.Google Scholar
Sørensen, Aage B., & Hallinan, Maureen T. (1976). A stochastic model for change in group structure. Social Science Research, 5, 43–61.Google Scholar
Stefani, R. (1997). Survey of the major world sports rating systems. Journal of Applied Statistics, 24, 635–646.Google Scholar
Strauss, D., & Ikeda, M. (1990). Pseudolikelihood estimation for social networks. Journal of the American Statistical Association, 85, 204–212.Google Scholar
Wang, Yuchung J., & Wong, George Y. (1987). Stochastic blockmodels for directed graphs. Journal of the American Statistical Association, 82, 8–19.Google Scholar
Wasserman, S., & Faust, K. (1994). Social Network Analysis. Cambridge, UK: Cambridge University Press.Google Scholar
Wasserman, S., & Pattison, P. (1996). Logit models and logistic regressions for social networks: I. An introduction to Markov random graphs and p*. Psychometrika, 61, 401–426.Google Scholar