Per Block

Reciprocity, transitivity, and the mysterious three-cycle

Abstract Reciprocity and transitivity are the two most important structural mechanisms underlying friendship network evolution. While on their own they are understood in great detail, the relation between them is rarely studied systematically. Are friendships outside of social groups more or less likely to be reciprocated than friendships embedded in a group? Using a theoretical framework that focusses on the situations in which friends interact and the social structures that stabilise one-sided friendships, I propose that the tendency towards reciprocation of friendships within transitive groups is usually lower than outside of transitive groups. In a meta-analysis of two datasets including 29 friendship networks using stochastic actor-oriented models (SAOMs), the interaction between reciprocity and transitivity is analysed. Supporting the theoretical reasoning, the interaction is consistently negative. Second, the tendency against forming three-cycles in friendship networks, which was consistently found in previous studies, is shown to be spurious and a result of neglecting to control for the tendency against reciprocation in transitive groups. The tendency against three-cycles is commonly seen as an indicator that unreciprocated friendships indicate local hierarchy differences between individuals; this proposition has to be re-evaluated in light of the findings of this study. Future studies that analyse the evolution of friendship networks should consider modelling reciprocation in transitive triplets and potentially omit modelling three-cycles.

Infection-induced behavioural changes reduce connectivity and the potential for disease spread in wild mice contact networks.

Infection may modify the behaviour of the host and of its conspecifics in a group, potentially altering social connectivity. Because many infectious diseases are transmitted through social contact, social connectivity changes can impact transmission dynamics. Previous approaches to understanding disease transmission dynamics in wild populations were limited in their ability to disentangle different factors that determine the outcome of disease outbreaks. Here we ask how social connectivity is affected by infection and how this relationship impacts disease transmission dynamics. We experimentally manipulated disease status of wild house mice using an immune challenge and monitored social interactions within this free-living population before and after manipulation using automated tracking. The immune-challenged animals showed reduced connectivity to their social groups, which happened as a function of their own behaviour, rather than through conspecific avoidance. We incorporated these disease-induced changes of social connectivity among individuals into models of disease outbreaks over the empirically-derived networks. The models revealed that changes in host behaviour frequently resulted in the disease being contained to very few animals, as opposed to becoming widespread. Our results highlight the importance of considering the role that behavioural alterations during infection can have on social dynamics when evaluating the potential for disease outbreaks.

Multidimensional homophily in friendship networks

Homophily - the tendency for individuals to associate with similar others - is one of the most persistent findings in social network analysis. Its importance is established along the lines of a multitude of sociologically relevant dimensions, e.g. sex, ethnicity and social class. Existing research, however, mostly focuses on one dimension at a time. But people are inherently multidimensional, have many attributes and are members of multiple groups. In this article, we explore such multidimensionality further in the context of network dynamics. Are friendship ties increasingly likely to emerge and persist when individuals have an increasing number of attributes in common? We analyze eleven friendship networks of adolescents, draw on stochastic actor-oriented network models and focus on the interaction of established homophily effects. Our results indicate that main effects for homophily on various dimensions are positive. At the same time, the interaction of these homophily effects is negative. There seems to be a diminishing effect for having more than one attribute in common. We conclude that studies of homophily and friendship formation need to address such multidimensionality further.

Relationship Reciprocation Modulates Resource Allocation in Adolescent Social Networks: Developmental Effects.

Adolescence is characterized as a period of social reorientation toward peer relationships, entailing the emergence of sophisticated social abilities. Two studies (Study 1: N = 42, ages 13–17; Study 2: N = 81, ages 13–16) investigated age group differences in the impact of relationship reciprocation within school‐based social networks on an experimental measure of cooperation behavior. Results suggest development between mid‐ and late adolescence in the extent to which reciprocation of social ties predicted resource allocation. With increasing age group, investment decisions increasingly reflected the degree to which peers reciprocated feelings of friendship. This result may reflect social‐cognitive development, which could facilitate the ability to navigate an increasingly complex social world in adolescence and promote positive and enduring relationships into adulthood.

Change we can believe in: Comparing longitudinal network models on consistency, interpretability and predictive power

Abstract While several models for analysing longitudinal network data have been proposed, their main differences, especially regarding the treatment of time, have not been discussed extensively in the literature. However, differences in treatment of time strongly impact the conclusions that can be drawn from data. In this article we compare auto-regressive network models using the example of TERGMs – a temporal extensions of ERGMs – and process-based models using SAOMs as an example. We conclude that the TERGM has, in contrast to the ERGM, no consistent interpretation on tie-level probabilities, as well as no consistent interpretation on processes of network change. Further, parameters in the TERGM are strongly dependent on the interval length between two time-points. Neither limitation is true for process-based network models such as the SAOM. Finally, both compared models perform poorly in out-of-sample prediction compared to trivial predictive models.

Dynamic Network Actor Models: Investigating Coordination Ties through Time:

Important questions in the social sciences are concerned with the circumstances under which individuals, organizations, or states mutually agree to form social network ties. Examples of these coordination ties are found in such diverse domains as scientific collaboration, international treaties, and romantic relationships and marriage. This article introduces dynamic network actor models (DyNAM) for the statistical analysis of coordination networks through time. The strength of the models is that they explicitly address five aspects about coordination networks that empirical researchers will typically want to take into account: (1) that observations are dependent, (2) that ties reflect the opportunities and preferences of both actors involved, (3) that the creation of coordination ties is a two-sided process, (4) that data might be available in a time-stamped format, and (5) that processes typically differ between tie creation and dissolution (signed processes), shorter and longer time windows (windowed processes), and initial and repeated creation of ties (weighted processes). Two empirical case studies demonstrate the potential impact of DyNAM models: The first is concerned with the formation of romantic relationships in a high school over 18 months, and the second investigates the formation of international fisheries treaties from 1947 to 2010.

Forms of Dependence: Comparing SAOMs and ERGMs From Basic Principles

Two approaches for the statistical analysis of social network generation are widely used; the tie-oriented exponential random graph model (ERGM) and the stochastic actor-oriented model (SAOM) or Siena model. While the choice for either model by empirical researchers often seems arbitrary, there are important differences between these models that current literature tends to miss. First, the ERGM is defined on the graph level, while the SAOM is defined on the transition level. This allows the SAOM to model asymmetric or one-sided tie transition dependence. Second, network statistics in the ERGM are defined globally but are nested in actors in the SAOM. Consequently, dependence assumptions in the SAOM are generally stronger than in the ERGM. Resulting from both, meso- and macro-level properties of networks that can be represented by either model differ substantively and analyzing the same network employing ERGMs and SAOMs can lead to distinct results. Guidelines for theoretically founded model choice are suggested.

Social interaction and pain: An arctic expedition

Complex human behaviour can only be understood within its social environment. However, disentangling the causal links between individual outcomes and social network position is empirically challenging. We present a research design in a closed real-world setting with high-resolution temporal data to understand this interplay within a fundamental human experience - physical pain. Study participants completed an isolated 3-week hiking expedition in the Arctic Circle during which they were subject to the same variation in environmental conditions and only interacted amongst themselves. Adolescents provided daily ratings of pain and social interaction partners. Using longitudinal network models, we analyze the interplay between social network position and the experience of pain. Specifically, we test whether experiencing pain is linked to decreasing popularity (increasing isolation), whether adolescents prefer to interact with others experiencing similar pain (homophily), and whether participants are increasingly likely to report similar pain as their interaction partners (contagion). We find that reporting pain is associated with decreasing popularity - interestingly, this effect holds for males only. Further exploratory analyses suggest this is at least partly driven by males withdrawing from contact with females when in pain, enhancing our understanding of pain and masculinity. Contrary to recent experimental and clinical studies, we found no evidence of pain homophily or contagion in the expedition group.

Rejoinder: DyNAMs and the Grounds for Actor-oriented Network Event Models:

Dynamic Event Processes in Social Networks. Karlsruhe, Germany: KIT Scientific. Tranmer, M., C. S. Marcum, F. B. Morton, D. P. Croft, and S. R. de Kort. 2015. “Using the Relational Event Model (REM) to Investigate the Temporal Dynamics of Animal Social Networks.” Animal Behaviour 101:99–105. Vu, D., A. Lomi, D. Mascia, and F. Pallotti. 2017. “Relational Event Models for Longitudinal Network Data with an Application to Interhospital Patient Transfers.” Statistics in Medicine 36(14):2265–87. Vu, D., P. Pattison, and G. Robins. 2015. “Relational Event Models for Social Learning in MOOCs.” Social Networks 43:121–35.