A dyadic reciprocity index for repeated interaction networks

PLOS ONE

While most social network research focuses on positive relational ties, such as friendship and information exchange, scholars are beginning to examine the dark side of human interaction, where negative connections represent different forms of interpersonal conflict, intolerance, and abuse. Despite this recent work, the extent to which positive and negative social network structure differs remains unclear. The current project considers whether a network’s small-scale, structural patterns of reciprocity, transitivity, and skew, or its “structural signature,” can distinguish positive versus negative links. Using exponential random graph models (ERGMs), we examine these differences across a sample of twenty distinct, negative networks and generate comparisons with a related set of twenty positive graphs. Relational ties represent multiple types of interaction such as like versus dislike in groups of adults, friendship versus cyberaggression among adolescents, and agreements versus dispu...

Understanding the dynamics of reciprocation is of great interest in sociology and computational social science. The recent growth of Massively Multi-player Online Games (MMOGs) has provided unprecedented access to large-scale data which enables us to study such complex human behavior in a more systematic manner. In this paper, we consider three different networks in the EverQuest2 game: chat, trade, and trust. The chat network has the highest level of reciprocation (33%) because there are essentially no barriers to it. The trade network has a lower rate of reciprocation (27%) because it has the obvious barrier of requiring more goods or money for exchange; morever, there is no clear benefit to returning a trade link except in terms of social connections. The trust network has the lowest reciprocation (14%) because this equates to sharing certain within-game assets such as weapons, and so there is a high barrier for such connections because they require faith in the players that are granted such high access. In general, we observe that reciprocation rate is inversely related to the barrier level in these networks. We also note that reciprocation has connections across the heterogeneous networks. Our experiments indicate that players make use of the medium-barrier reciprocations to strengthen a relationship. We hypothesize that lower-barrier interactions are an important component to predicting higherbarrier ones. We verify our hypothesis using predictive models for trust reciprocations using features from trade interactions. Using the number of trades (both before and after the initial trust link) boosts our ability to predict if the trust will be reciprocated up to 11% with respect to the AUC. More generally, we see strong correlations across the different networks and emphasize that network dynamics, such as reciprocation, cannot be studied in isolation on just a single type of connection.

Evolution, 2012

lack the information or cognitive skills needed for other types of reciprocity. Yet, generalized reciprocity is anonymous and thus defenseless against exploitation by defectors. Recognizing that animals hardly ever interact randomly, we investigate whether social network structure can mitigate this vulnerability. Our results show that heterogeneous interaction patterns strongly support the evolution of generalized reciprocity. The future probability of being rewarded for an altruistic act is inversely proportional to the average connectivity of the social network when cooperators are rare. Accordingly, sparse networks are conducive to the invasion of reciprocal altruism. Moreover, the evolutionary stability of cooperation is enhanced by a modular network structure. Communities of reciprocal altruists are protected against exploitation, because modularity increases the mean access time, that is, the average number of steps that it takes for a random walk on the network to reach a defector. Sparseness and community structure are characteristic properties of vertebrate social interaction patterns, as illustrated by network data from natural populations ranging from fish to primates.

Quality & Quantity, 2007

We introduce measures and statistical tests for multiplexity and exchange that are modeled on similar ideas developed for reciprocity quite early in the history of social network research. As properties of a multi-relation network, multiplexity, and exchange have almost as ancient a history as reciprocity, but have not been as intensively investigated from a methodological perspective. Multiplexity refers to the

Three mechanisms have been proposed to underlie reciprocation of social behaviors in gregarious animals: " calculated reciprocity, " " emotional bookkeeping, " and " symmetry-based reciprocity. " Among these explanations, emotional book-keeping has received the broadest support from experimental and observational studies. On the other hand, 3 individual-based models have shown that recipro-cation may emerge via " symmetry-based reciprocity, " " emotional bookkeeping, " or a combination of both mechanisms. Here, we use these 3 models to assess their relative fit with empirical data on reciprocation and social network structure across different groups and species of macaques. We collected grooming data from 14 groups and 8 macaque species and simulated each group in each model. We analyzed and quantitatively compared social network metrics of the empirical and the models' grooming networks. The 3 models captured fairly well the features of observed networks, and fitted data from wild groups better than captive ones. The emotional bookkeeping model seemed on average to fit slightly better the social networks metrics observed in empirical data, but failed to reproduce some grooming patterns. The symmetry-based models, on the other hand, fitted better other network parameters (e.g., mod-ularity). No model generally fitted the data better than the others, and the fit with some metrics (e.g., modularity, centralization index) was low even after optimization. Thus, our analyses indicate that in the models social interactions may be simpler than in reality and models may miss social processes (e.g., third-party awareness).

2009

2011

We present a study of the reciprocity of human behaviour based on mobile phone usage records. The underlying question is whether human relationships are mutual, in the sense that both are equally active in keeping up the relationship, or is it on the contrary typical that relationships are lopsided, with one party being significantly more active than the other. We study this question with the help of a mobile phone data set consisting of all mobile phone calls between 5.3 million customers of a single mobile phone operator. It turns out that lopsided relations are indeed quite common, to the extent that the variation cannot be explained by simple random deviations or by variations in personal activity. We also show that there is no non-trivial correlation between reciprocity and local network density.

2007

We explore the effects of social distance in experiments conducted over the Internet on three continents, in classroom laboratory sessions conducted in Israel and Spain, and in computer sessions pairing participants from different states, one in Texas and the other in California. Our design elicits individual behavior profiles over a range of contingencies, enabling us to identify heterogeneity among our participants. We find that many people show regard for others, even with the apparent social distance inherent with Internet interaction. In all cases, a substantial minority makes choices indicating positive reciprocity; the proportion doing so varies inversely with social distance.

Quality & Quantity, 2010

This paper examines statistical analysis of social reciprocity, that is, the balance between addressing and receiving behaviour in social interactions. Specifically, it focuses on the measurement of social reciprocity by means of directionality and skew-symmetry statistics at different levels. Two statistics have been used as overall measures of social reciprocity at group level: the directional consistency and the skew-symmetry statistics. Furthermore, the skew-symmetry statistic allows social researchers to obtain complementary information at dyadic and individual levels. However, having computed these measures, social researchers may be interested in testing statistical hypotheses regarding social reciprocity. For this reason, it has been developed a statistical procedure, based on Monte Carlo sampling, in order to allow social researchers to describe groups and make statistical decisions.