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A dyadic reciprocity index for repeated interaction networks*

Published online by Cambridge University Press:  15 April 2013

CHENG WANG ,
OMAR LIZARDO ,
DAVID HACHEN ,
ANTHONY STRATHMAN ,
ZOLTÁN TOROCZKAI  and
NITESH V. CHAWLA
CHENG WANG
Affiliation:
Department of Sociology, University of Notre Dame, 810 Flanner Hall, Notre Dame, IN 46556, USA Interdisciplinary Center for Network Science and Applications (ICeNSA), 384E Nieuwland Science Hall, Notre Dame, IN 46556, USA (e-mail: cwang3@nd.edu, olizardo@nd.edu, dshachen@nd.edu)
OMAR LIZARDO
Affiliation:
Department of Sociology, University of Notre Dame, 810 Flanner Hall, Notre Dame, IN 46556, USA Interdisciplinary Center for Network Science and Applications (ICeNSA), 384E Nieuwland Science Hall, Notre Dame, IN 46556, USA (e-mail: cwang3@nd.edu, olizardo@nd.edu, dshachen@nd.edu)
DAVID HACHEN
Affiliation:
Department of Sociology, University of Notre Dame, 810 Flanner Hall, Notre Dame, IN 46556, USA Interdisciplinary Center for Network Science and Applications (ICeNSA), 384E Nieuwland Science Hall, Notre Dame, IN 46556, USA (e-mail: cwang3@nd.edu, olizardo@nd.edu, dshachen@nd.edu)
ANTHONY STRATHMAN
Affiliation:
Department of Physics, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA Interdisciplinary Center for Network Science and Applications (ICeNSA), 384E Nieuwland Science Hall, Notre Dame, IN 46556, USA (e-mail: astrathm@nd.edu, toro@nd.edu)
ZOLTÁN TOROCZKAI
Affiliation:
Department of Physics, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA Interdisciplinary Center for Network Science and Applications (ICeNSA), 384E Nieuwland Science Hall, Notre Dame, IN 46556, USA (e-mail: astrathm@nd.edu, toro@nd.edu)
NITESH V. CHAWLA
Affiliation:
Department of Computer Science and Engineering, College of Engineering, University of Notre Dame, 384 Fitzpatrick Hall, Notre Dame, IN 46556, USA Interdisciplinary Center for Network Science and Applications (ICeNSA), 384E Nieuwland Science Hall, Notre Dame IN 46556, USA (e-mail: nchawla@nd.edu)
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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.

Keywords

reciprocityweighted networksinteractionweak tiesassortativity
Type
Research Article
Information
Network Science , Volume 1 , Issue 1 , April 2013 , pp. 31 - 48
Copyright
Copyright © Cambridge University Press 2013

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Footnotes

*

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.

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