The redundancy of a system denotes the amount of duplicate components or mechanisms in it. For a network, especially one in which mass or information is being transferred from an origin to a destination, redundancy is related to the robustness of the system. Existing network measures of redundancy rely on local connectivity (e.g. clustering coefficients) or the existence of multiple paths. As in many systems there are functional dependencies between components and paths, a measure that not only characterizes the topology of a network, but also takes into account these functional dependencies, becomes most desirable.

We propose a network redundancy measure in a prototypical model that contains functionally dependent directed paths: a Boolean model of a signal transduction network. The functional dependencies are made explicit by using an expanded network and the concept of elementary signaling modes (ESMs). We define the redundancy of a Boolean signal transduction network as the maximum number of node-independent ESMs and develop a methodology for identifying all maximal node-independent ESM combinations. We apply our measure to a number of signal transduction network models and show that it successfully distills known properties of the systems and offers new functional insights. The concept can be easily extended to similar related forms, e.g. edge-independent ESMs.

Models of network evolution are based on the implicit assumption that network growth is continuous, uniform, and steady. Using the data collected from a large online-blogging platform, we show that the addition and removal of network ties by users do not occur sporadically at isolated nodes spread all over the network, as assumed by the vast majority of stochastic network models, but rather occur in brief bursts of intense local activity.

These bursts of network growth and attrition (addition and removal of network ties) are highly localized around focal nodes. Such network changes coincide with nearly instantaneous densification of the ties between the affected nodes, resulting in an increase of local clustering. Furthermore, we find that these network changes are tightly coupled to the dynamics of individual attributes, particularly the increase in homology between neighboring nodes (homophily) within the scope of the burst. Coincidence of the localized network change with the increase in homophily suggests a strong coupling between the selection and influence processes that lead to simultaneous elevation of assortativity and clustering.

Social networks, particularly those defined by friendships, influence many childhood and adolescent health behaviors such as the use of alcohol, tobacco, and other drugs, as well as diet and physical activity. Few, if any, studies have examined the concordance between friendship networks and sun exposure/safety behaviors. This study examines the friendship networks and sun safety behaviors for a group of fourth and fifth grade students taking part in a larger sun safety intervention, “SunSmart” (n = 128). Intra-class correlation, homophily hypothesis testing, and exponential random graph models were used to test friendship homophily based on sun safety behaviors. Peer Leaders were identified through social network popularity, and sun safety change scores were compared between Peer Leaders and non-leaders. Results show that students cluster based on shared demographic characteristics and some sun safety behaviors, and that there was a trend for Peer Leaders to respond better to the SunSmart intervention than non-leaders. Implications for future sun safety interventions using Peer Leaders as champions for sun safety behavior change are discussed.

Social networks influence children and adolescents' physical activity. The focus of this paper is to examine the differences in the effects of physical activity on friendship selection, with eye to the implications on physical activity interventions for young children. Prior to implementing a network intervention in the field, it is important to understand potential heterogeneities in the effects that activity level have on network structure. In this study, the associations between activity level and cross-sectional network structure, and activity level and change in network structure are assessed. We studied a real-world friendship network among 81 children (average age 7.96 years) who lived in low SES neighborhoods, attended public schools, and attended one of two structured aftercare programs, of which one has existed and the other was new. We modeled network selection effects and cross-sectional properties, while accounting for potential heterogeneities between networks. There was heterogeneity in the effect of physical activity on both cross-sectional network structure and the formation and dissolution processes, both across time and between networks. This suggests that if peer selection processes are changing within a network, a static network intervention strategy for childhood physical activity could become inefficient as the network evolves.

Despite the pivotal role that both power and interpersonal trust play in a multitude of social exchange situations, relatively little is known about their interplay. Moreover, previous theorizing makes competing claims. Do we consider our relatively more powerful exchange partners to be less trustworthy, as rational choice reasoning would suggest? Or do more complex psychological mechanisms lead us to trust them more, as motivated cognition reasoning implies? Extending the latter approach, we develop and empirically test three hypotheses on the interrelation between perceptions of interpersonal trust and power. According to the status value hypothesis, individuals are more likely to befriend those whom they or others perceive as powerful. The status signaling hypothesis states that the friends of people one perceives as powerful will also be seen as powerful. According to the self-monitoring hypothesis, high self-monitors are more likely than low self-monitors to befriend those they or others perceive as powerful. We use multiplex stochastic actor-based models to analyze the co-evolution of trust and power relations among n = 49 employees in a Dutch Youth Care organization. Data covers three waves of a longitudinal sociometric network survey collected over a period of 18 months in the years 2009–2010. In general, we find some support for all three hypotheses, though the effects are weak. Being one of the first organizational field studies on the co-evolution of power and trust, we conclude with discussing the implications of these findings for the study of social exchange processes.

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by the beforehand averaged adjacency matrix over samples of growing networks as a new general framework for investigating the characteristic quantities. It is applied to some network models, and shows a good approximation of degree distribution asymptotically. In particular, our approach will be applicable through the numerical calculations instead of intractable theoretical analyses, when the time-course of degree is a monotone increasing function like power law or logarithm.