Breadth of Peer Relationships 1 Running head : EXTERNALIZING PRESCHOOLERS ’ SOCIAL BREADTH The Breadth of Peer Relationships among Externalizing Preschoolers : An Illustration of the Q-Connectivity Method

We studied the relations between externalizing-related behaviors and social breadth (the number of peers children interact with and the extent to which they maintain interactions over time) in preschoolers. Using the Q-connectivity method to assess social breadth, which is a variation on social network analysis, we explored how externalizing-related behaviors varied in relation to: 1) the continuity of social breadth and 2) patterns of decline in social breadth across time. Findings suggested that externalizing preschoolers were less likely than their non-externalizing peers to maintain continuity in peer interactions across time. The findings contribute to an understanding of externalizing preschoolers’ social breadth and time spent with peers. The utility of the Qconnectivity method for future research is also discussed. Breadth of Peer Relationships 3 The Breadth of Peer Relationships among Externalizing Preschoolers: An Illustration of the QConnectivity Method One challenge faced by contemporary researchers interested in social interactions is understanding how exposure to externalizing peers contributes to the spread of aggression and related problem behaviors. This issue has important implications for prevention scientists, who have found the effectiveness of intervention programs hindered by peer contagion processes (Dishion, Spracklen, Andrews, & Patterson, 1996; Poulin, Dishion, & Burraston, 2001), as well as for educators, who recognize that classroom social norms supporting aggressive behavior can undermine the learning environment (Henry et al., 2000). Central to understanding how peer contagion processes operate is an awareness of the potential extent of influence that externalizing children have on their peers. Thus, it is necessary to understand how far-reaching externalizing children’s connections are with their peers – how many peers externalizing children interact with and the extent to which they maintain interactions with peers over time. In the present study, we explored the breadth of young externalizing children’s relationships with peers. To do so, we used the Q-connectivity method (Barcelo & Laubenbacher, 2005), a variation on social network methods that capitalizes on multiple samples of social networks over time, which can be used to calculate social breadth. Specifically, in this study, we collected numerous observations of children’s peer interactions over time, providing an extensive picture of the dynamics of peer interactions. An additional unique feature of this study is that we drew on a sample of preschoolers; this age group has been relatively neglected in past research in this area (see Hanish, Martin, Fabes, Leonard, & Herzog, 2005; Snyder, Horsch, & Childs, 1997 for exceptions), although the peer relationships of young children lay the foundation for their later peer experiences. Social Breadth and Externalizing Behavior in Early Childhood Breadth of Peer Relationships 4 One of the most interesting, but least well studied, aspects of children’s peer relationships is the substantial variation in the breadth of children’s peer affiliations. Children are most likely to engage peers who are similar to themselves on demographic dimensions, such as sex, and behavioral dimensions, such as aggressiveness (Cairns, Cairns, Neckerman, & Gest, 1988; Espelage, Holt, & Henkel, 2003); yet, with numerous peers in a class to choose as affiliation partners, there is marked individual variation in the number and types of peers with whom children interact. Thus, it is not surprising that some peers never interact with one another whereas others interact frequently (Snyder, West, Stockemer, & Gibbons, 1996). To complicate matters, relationship patterns change over time: friendships form, persist for short or long periods of time, and often dissolve; peers move into or out of social networks; and children’s social positions can become more or less prominent over time. Consequently, there is both stability and fluidity in children’s peer affiliations over shorter (e.g., moment-to-moment, week-to-week), and longer (e.g., month-to-month, year-to-year) periods of time (Cairns, Leung, Buchanan, & Cairns, 1995; Estell, Cairns, Farmer, & Cairns, 2002; Martin, Fabes, Hanish, & Hollenstein, 2005). These features of children’s peer relationships contribute to substantial individual variability in the breadth of children’s peer affiliations and the persistence of these affiliations across time, and likely contribute to important developmental outcomes. It is this variability in young children’s social breadth that we highlight in the present study. Social breadth refers to the range of peer affiliates – that is, the number of peers that each child interacts with – and the extent to which these peer affiliations are observed over time. As such, social breadth represents a construct that is distinct from conceptions of friendship, social status, or membership in social networks because it reflects the comprehensiveness of children’s peer affiliations (and the maintenance of these affiliations over time) rather than affective mutuality, behavioral homophily, or the quality of their relationships per se, although it may Breadth of Peer Relationships 5 relate to these factors. The roots of this construct can be seen in the work of Waldrop and Halverson (1975), who studied the extensiveness of peer relationships. From a developmental perspective, social breadth reflects a particularly central feature of children’s peer relationships during the preschool period. It is during these years that children move away from a general tendency to play alone or along side other children and begin to engage in increasing levels of social interactive play (Rubin, Bukowski, & Parker, 1998). This is reflected in the fact that preschoolers’ social networks become larger, more dense, and more organized with age (Strayer & Santos, 1996; Vespo, Kerns, & O'Connor, 1996). Thus, we would expect great variability in social breadth among young children, as some children begin to develop large, comprehensive, and stable peer networks, and others, who may be more immature or less socially skilled, are less likely to engage with peers. There is reason to believe that social breadth varies in relation to young children’s externalizing behaviors. Prior studies have indicated that structural aspects of preschool children’s peer relationships are related to their exhibition of externalizing behaviors, such that the peer relationships of aggressive children tend to be more sparse and less stable over time. For instance, van den Oord, Rispens, Goudena, and Vermande (2000), who collected sociometric nomination data with over 1000 preschool children, found that children who were less likely to be members of cliques and children whose peer relationships were less transitive (i.e., children who were disliked by their friends’ friends) were rated by teachers as displaying more problem behaviors (e.g., aggression, attention problems, and fear). Similarly, Snyder et al. (1997) found that aggressive preschoolers, compared to nonaggressive preschoolers, developed fewer relationships with peers that were stable over time. Additionally, studies have demonstrated that aggressive children have lower social preference scores and are more likely to be rejected by peers than their nonaggressive counterparts (Olson, 1992; Snyder et al., 1997). Thus, we expect Breadth of Peer Relationships 6 social breadth to be negatively related to externalizing behaviors and positively related to regulatory abilities (a correlate of externalizing behavior) among young children. The Use of the Q-Connectivity Method to Measure Social Breadth Social network methods have demonstrated utility for identifying the structural dimensions of children’s peer relationships (e.g., membership in or isolation from social networks, network centrality, the social distance connecting a child to his or her peers, etc.). Most often, social network data have been obtained using sociometric nominations collected at one discrete time; thus, the resulting social networks represent aggregated views of relationships that provide relatively static pictures of children’s affiliation patterns at that particular point in time (e.g., Cairns et al., 1988). Recently, however, we have seen the development of new social network methodologies that facilitate the use of data collected at multiple points in time (e.g., Moody, McFarland, & Bender-deMoll, 2005; Huisman & Snijders, 2003). This line of work, though still in its infancy, has the potential to enhance our understanding of social developmental processes above and beyond what can be learned from maps of social networks obtained at a single time. In the present study, we relied on observations of children’s peer interactional partners obtained over the course of a semester. These longitudinal observations lend themselves to an assessment of time-dependent social processes, and we used the Q-connectivity method as a basis for calculating children’s social breadth over time. Compared to traditional social network analysis methods, the Q-connectivity method allows for a more extensive view of the dynamics of interaction patterns rather than simply structural features of these patterns. The Q-connectivity method involves translating mathematical theory into techniques that can be used to measure children’s social patterns with classmates (or other specified group members) over time (Barcelo & Laubenbacher, 2005). It is based on the Q-connectivity theory for simplicial complexes, which is a method of representing dynamic (i.e., time-dependent) Breadth of Peer Relationships 7 processes as a series of graphs containing vertices (nodes) indicating agents (e.g., children) and edges linking related vertices to indicate connections among agents. It has been applied in diverse contexts such as epidemiological contact networks and search-and-rescue operations (Barcel