Skip to main content Accessibility help
×
Home

A dyadic reciprocity index for repeated interaction networks*

  • CHENG WANG (a1) (a2), OMAR LIZARDO (a1) (a2), DAVID HACHEN (a1) (a2), ANTHONY STRATHMAN (a3) (a4), ZOLTÁN TOROCZKAI (a3) (a4) and NITESH V. CHAWLA (a5) (a6)...

Abstract

A wide variety of networked systems in human societies are composed of repeated communications between actors. A dyadic relationship made up of repeated interactions may be reciprocal (both actors have the same probability of directing a communication attempt to the other) or non-reciprocal (one actor has a higher probability of initiating a communication attempt than the other). In this paper we propose a theoretically motivated index of reciprocity appropriate for networks formed from repeated interactions based on these probabilities. We go on to examine the distribution of reciprocity in a large-scale social network built from trace-logs of over a billion cell-phone communication events across millions of actors in a large industrialized country. We find that while most relationships tend toward reciprocity, a substantial minority of relationships exhibit large levels of non-reciprocity. This is puzzling because behavioral theories in social science predict that persons will selectively terminate non-reciprocal relationships, keeping only those that approach reciprocity. We point to two structural features of human communication behavior and relationship formation—the division of contacts into strong and weak ties and degree-based assortativity—that either help or hinder the ability of persons to obtain communicative balance in their relationships. We examine the extent to which deviations from reciprocity in the observed network are partially traceable to the operation of these countervailing tendencies.

Copyright

Footnotes

Hide All
*

Research was sponsored by the Army Research Laboratory and was accomplished in part under Cooperative Agreement Number W911NF-09-2-0053, by the Defense Threat Reduction Agency (DTRA) grant HDTRA 1-09-1-0039 (Anthony Strathman and Zoltán Toroczkai), and by the National Science Foundation (NSF) grant BCS-0826958. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. Special acknowledgments go to Albert László Barabási for providing the source data.

Footnotes

References

Hide All
Almaas, E., Kovács, B., Vicsek, T., Oltvai, Z. N., & Barabási, A. L. (2004). Letters to nature-global organization of metabolic fluxes in the bacterium ewhedchia coli. Nature, 427 (6977), 839842.
Aral, S., & Van Alstyne, M. (2011). The diversity-bandwidth tradeoff. American Journal of Sociology, 117 (1), 90171.
Ball, B., & Newman, M. E. J. (2013). Friendship networks and social status. Network Science, 1 (1), (this issue).
Barabasi, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286 (5439), 509.
Barrat, A., Barthelemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, 101 (11), 37473752.
Barthelemy, M., Gondran, B., & Guichard, E. (2003). Spatial structure of the internet traffic. Physica A: Statistical Mechanics and Its Applications, 319, 633642.
Barthélemy, M., Barrat, A., Pastor-Satorras, R., & Vespignani, A. (2005). Characterization and modeling of weighted networks. Physica A: Statistical Mechanics and Its Applications, 346 (1–2), 3443.
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D. U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424 (4–5), 175308.
Borgatti, S. P. (2005). Centrality and network flow. Social Networks, 27 (1), 5571.
Borgatti, S. P., Mehra, A., Brass, D. J., & Labianca, G. (2009). Network analysis in the social sciences. Science, 323 (5916), 892.
Carley, K. M., & Krackhardt, D. (1996). Cognitive inconsistencies and non-symmetric friendship. Social Networks, 18 (1), 127.
Catanzaro, M., Caldarelli, G., & Pietronero, L. (2004). Assortative model for social networks. Physical Review E, 70 (3), 037101.
Colizza, V., Flammini, A., Serrano, M. A., & Vespignani, A. (2006). Detecting rich-club ordering in complex networks. Nature Physics, 2 (2), 110115.
Csermely, P. (2004). Strong links are important, but weak links stabilize them. Trends in Biochemical Sciences, 29 (7), 331334.
Csermely, P. (2006). Weak links: stabilizers of complex systems from proteins to social networks. Heidelberg, Germany: Springer-Verlag.
Davis, James A. (1963). Structural balance, mechanical solidarity, and interpersonal relations. American Journal of Sociology, 68, 444462.
Davis, J. A. (1979). The Davis/Holland/Leinhardt studies: An overview. In Holland, P. W. & Leinhardt, S. (Eds.), Perspectives on social network research (pp. 5162). New York: Academic Press.
Doreian, P. (2002). Event sequences as generators of social network evolution. Social Networks, 24 (2), 93119.
Eagle, N., Pentland, A. S., & Lazer, D. (2008). Mobile phone data for inferring social network structure. In Liu, H., Salerno, J. J. & Young, M. J. (Eds.), Social Computing, Behavioral Modeling and Prediction (pp. 7988). New York: Springer.
Eagle, N., Pentland, A. S., & Lazer, D. (2009). Inferring friendship network structure by using mobile phone data. Proceedings of the National Academy of Sciences, 106 (36), 15274.
Feld, Scott L. (1981). The focused organization of social ties. American Journal of Sociology, 86, 10151035.
Freeman, L. C., Borgatti, S. P., & White, D. R. (1991). Centrality in valued graphs: A measure of betweenness based on network flow. Social Networks, 13 (2), 141154.
Garlaschelli, D., & Loffredo, M. I. (2004). Patterns of link reciprocity in directed networks. Physical Review Letters, 93 (26), 268701.
Gould, Roger V. (2002). The origins of status hierarchies: A formal theory and empirical test. American Journal of Sociology, 107 (5), 11431178.
Gouldner, Alvin W. (1960). The norm of reciprocity: A preliminary statement. American Sociological Review, 25 (2), 161178.
Granovetter, Mark S. (1973). The strength of weak ties. American Journal of Sociology, 78 (6), 13601380.
Hallinan, Maureen T. (1978). The process of friendship formation. Social Networks, 1, 193210.
Hallinan, M. T., & Hutchins, E. E. (1980). Structural effects on dyadic change. Social Forces, 59 (1), 225245.
Hammer, M. (1985). Implications of behavioral and cognitive reciprocity in social network data. Social Networks, 7, 189201.
Heider, F. (1958). The psychology of interpersonal relations. New York: Wiley.
Herfindahl, Orris C. (1950). Concentration in the steel industry. PhD thesis, Columbia University, New York, NY.
Karsai, M., Kaski, K., & Kertész, J. (2012). Correlated dynamics in egocentric communication networks. Plos One, 7 (7), e40612.
Kossinets, G., & Watts, D. J. (2006). Empirical analysis of an evolving social network. Science, 311 (5757), 8890.
Kovanen, L., Saramaki, J., & Kaski, K. (2010). Reciprocity of mobile phone calls. arxiv preprint, arxiv:1002.0763.
Krackhardt, D. (1987). Cognitive social structures. Social Networks, 9 (2), 109134.
Mandel, M. (2000). Measuring tendency towards mutuality in a social network. Social Networks, 22 (4), 285298.
Marsden, Peter V. (1987). Core discussion networks of Americans. American Sociological Review, 52 (1), 122131.
Marsden, P. V., & Campbell, K. E. (1984). Measuring tie strength. Social Forces, 63, 482501.
Martin, J. L. (2009). Social structures. Princeton, NJ: Princeton University Press.
Maslov, S., & Sneppen, K. (2002). Specificity and stability in topology of protein networks. Science, 296 (5569), 910913.
Newcomb, T. M. (1961). The acquaintance process. New York: Holt, Rinehart and Winston.
Newcomb, Theodore M. (1968). Interpersonal balance. In Abelson, R. P., Aronson, E., McGiure, W. J., Newcomb, T. M., Rosenberg, M. J. & Tannenbaum, O. H. (Eds.), Theories of cognitive consistency (pp. 2851). New York: Holt, Rinchart & Winston.
NewcombTheodore, M. Theodore, M. (1979). Reciprocity of interpersonal attraction: A non-confirmation of a plausible hypothesis. Social Psychology Quarterly, 42, 299306.
Newman, M. E. J. (2002). Assortative mixing in networks. Physical Review Letters, 89 (20), 208701.
Newman, Mark E. J. (2003). Mixing patterns in networks. Physical Review E, 67 (2), 26126.
Newman, M. E. J., & Park, J. (2003). Why social networks are different from other types of networks. Physical Review E, 68 (3), 36122.
Park, J., & Newman, M. E. J. (2003). Origin of degree correlations in the internet and other networks. Physical Review E, 68 (2), 26112.
Peay, E. R. (1980). Connectedness in a general model for valued networks. Social Networks, 2 (4), 385410.
Schaefer, David R. (2012). Homophily through nonreciprocity: Results of an experiment. Social Forces, 90 (4), 12711295.
Serrano, M. A., Boguñá, M., & Vespignani, A. (2009). Extracting the multiscale backbone of complex weighted networks. Proceedings of the National Academy of Sciences, 106 (16), 64836488.
Skvoretz, J., & Agneessens, F. (2007). Reciprocity, multiplexity, and exchange: Measures. Quality and Quantity, 41 (3), 341357.
Waller, W. (1937). The rating and dating complex. American Sociological Review, 2 (5), 727734.
Wasserman, S., & Faust, K. (1994). Social network analysis: methods and applications. Cambridge, UK: Cambridge University Press.
Wellman, B., & Wortley, S. (1990). Different strokes from different folks: Community ties and social support. American Journal of Sociology, 96, 558588.
Wu, Y., Zhou, C., Xiao, J., Kurths, J., & Schellnhuber, H. J. (2010). Evidence for a bimodal distribution in human communication. Proceedings of the National Academy of Sciences, 107 (44), 1880318808.
Xu, X. K., Wang, J. B., Wu, Y., & Small, M. (2012). Pairwise interaction pattern in the weighted communication network. arxiv preprint, arxiv:1203.1105.
Yang, S., & Knoke, D. (2001). Optimal connections: strength and distance in valued graphs. Social Networks, 23 (4), 285295.
Yook, S. H., Jeong, H., Barabasi, A. L., & Tu, Y. (2001). Weighted evolving networks. Physical Review Letters, 86 (25), 58355838.
Zamora-López, G., Zlatić, V., Zhou, C., Štefančić, H., & Kurths, J. (2008). Reciprocity of networks with degree correlations and arbitrary degree sequences. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 77 (1), 016106.

Keywords

A dyadic reciprocity index for repeated interaction networks*

  • CHENG WANG (a1) (a2), OMAR LIZARDO (a1) (a2), DAVID HACHEN (a1) (a2), ANTHONY STRATHMAN (a3) (a4), ZOLTÁN TOROCZKAI (a3) (a4) and NITESH V. CHAWLA (a5) (a6)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed