We develop a model of strategic network formation of collaborations to analyze the consequences of an understudied but consequential form of heterogeneity: differences between actors in the form of their production functions. We also address how this interacts with resource heterogeneity, as a way to measure the impact actors have as potential partners on a collaborative project. Some actors (e.g., start-up firms) may exhibit increasing returns to their investment into collaboration projects, while others (e.g., established firms) may face decreasing returns. Our model provides insights into how actor heterogeneity can help explain well-observed collaboration patterns. We show that if there is a direct relation between increasing returns and resources, start-ups exclude mature firms and networks become segregated by types of production function, portraying dominant group architectures. On the other hand, if there is an inverse relation between increasing returns and resources, networks portray core-periphery architectures, where the mature firms form a core and start-ups with low-resources link to them.

Social relationships are important among persons experiencing homelessness, but there is little research on changes in social networks among persons moving into permanent supportive housing (PSH). Using data collected as part of a longitudinal study of 405 adults (aged 39+) moving into PSH, this study describes network upheaval during this critical time of transition. Interviews conducted prior to and after three months of living in PSH assessed individual-level (demographics, homelessness history, health, and mental health) and social network characteristics, including network size and composition (demographics, relationship type, and social support). Interviewers utilized network member characteristics to assess whether network members were new or sustained between baseline and three months post-housing. Multilevel logistic regression models assessed characteristics of network members associated with being newly gained or persisting in networks three months after PSH move-in. Results show only one-third of social networks were retained during the transition to PSH, and veterans, African Americans, and other racial/ethnic minorities, and those living in scattered site housing, were more likely to experience network disruption. Relatives, romantic partners, and service providers were most likely to be retained after move-in. Some network change was moderated by tie strength, including the retention of street-met persons. Implications are discussed.

Community-based physical activity programs, such as the Recreovía, are effective in promoting healthy behaviors in Latin America. To understand Recreovías’ challenges and scalability, we characterized its social network longitudinally while studying its participants’ social cohesion and interactions. First, we constructed the Main network of the program’s Facebook profile in 2013 to determine the main stakeholders and communities of participants. Second, we studied the Temporal network growth of the Facebook profiles of three Recreovía locations from 2008 to 2016. We implemented a Time Windows in Networks algorithm to determine observation periods and a scaling model of cities’ growth to measure social cohesion over time. Our results show physical activity instructors as the main stakeholders (20.84% nodes of the network). As emerging cohesion, we found: (1) incremental growth of Facebook users (43–272 nodes), friendships (55–2565 edges), clustering coefficient (0.19–0.21), and density (0.04–0.07); (2) no preferential attachment behavior; and (3) a social cohesion super-linear growth with 1.73 new friendships per joined user. Our results underscore the physical activity instructors’ influence and the emergent cohesion in innovation periods as a co-benefit of the program. This analysis associates the social and healthy behavior dimensions of a program occurring in natural environments under a systemic approach.

Superbubbles are acyclic induced subgraphs of a digraph with single entrance and exit that naturally arise in the context of genome assembly and the analysis of genome alignments in computational biology. These structures can be computed in linear time and are confined to non-symmetric digraphs. We demonstrate empirically that graph parameters derived from superbubbles provide a convenient means of distinguishing different classes of real-world graphical models, while being largely unrelated to simple, commonly used parameters.

We consider a dynamic network cascade process developed by Duncan Watts applied to a class of random networks, developed independently by Newman and Miller, which allows a specified amount of clustering (short loops). We adapt existing methods for locally tree-like networks to formulate an appropriate two-type branching process to describe the spread of a cascade started with a single active node and obtain a fixed-point equation to implicitly express the extinction probability of such a cascade. In so doing, we also recover a formula that has appeared in various forms in works by Hackett et al. and Miller which provides a threshold condition for certain extinction of the cascade. We find that clustering impedes cascade propagation for networks of low average degree by reducing the connectivity of the network, but for networks with high average degree, the presence of small cycles makes cascades more likely.

The validity of network observations is sometimes of concern in empirical studies, since observed networks are prone to error and may not represent the population of interest. This lack of validity is not just a result of random measurement error, but often due to systematic bias that can lead to the misinterpretation of actors’ preferences of network selections. These issues in network observations could bias the estimation of common network models (such as those pertaining to influence and selection) and lead to erroneous statistical inferences. In this study, we proposed a simulation-based sensitivity analysis method that can evaluate the robustness of inferences made in social network analysis to six forms of selection mechanisms that can cause biases in network observations—random, homophily, anti-homophily, transitivity, reciprocity, and preferential attachment. We then applied this sensitivity analysis to test the robustness of inferences for social influence effects, and we derived two sets of analytical solutions that can account for biases in network observations due to random, homophily, and anti-homophily selection.

Population analyses of functional connectivity have provided a rich understanding of how brain function differs across time, individual, and cognitive task. An important but challenging task in such population analyses is the identification of reliable features that describe the function of the brain, while accounting for individual heterogeneity. Our work is motivated by two particularly important challenges in this area: first, how can one analyze functional connectivity data over populations of individuals, and second, how can one use these analyses to infer group similarities and differences. Motivated by these challenges, we model population connectivity data as a multilayer network and develop the multi-node2vec algorithm, an efficient and scalable embedding method that automatically learns continuous node feature representations from multilayer networks. We use multi-node2vec to analyze resting state fMRI scans over a group of 74 healthy individuals and 60 patients with schizophrenia. We demonstrate how multilayer network embeddings can be used to visualize, cluster, and classify functional regions of the brain for these individuals. We furthermore compare the multilayer network embeddings of the two groups. We identify significant differences between the groups in the default mode network and salience network—findings that are supported by the triple network model theory of cognitive organization. Our findings reveal that multi-node2vec is a powerful and reliable method for analyzing multilayer networks. Data and publicly available code are available at https://github.com/jdwilson4/multi-node2vec.

A number of theoretical results have provided sufficient conditions for the selection of payoff-efficient equilibria in games played on networks when agents imitate successful neighbors and make occasional mistakes (stochastic stability). However, those results only guarantee full convergence in the long-run, which might be too restrictive in reality. Here, we employ a more gradual approach relying on agent-based simulations avoiding the double limit underlying these analytical results. We focus on the circular-city model, for which a sufficient condition on the population size relative to the neighborhood size was identified by Alós-Ferrer & Weidenholzer [(2006) Economics Letters, 93, 163–168]. Using more than 100,000 agent-based simulations, we find that selection of the efficient equilibrium prevails also for a large set of parameters violating the previously identified condition. Interestingly, the extent to which efficiency obtains decreases gradually as one moves away from the boundary of this condition.