We evaluate the effect of reciprocal trust within pairs of individuals—gauged by total potential earnings in a trust experiment—on the probability of relationship formation, in comparison with well-known determinants of social ties, such as time of exposure and homophily along demographic traits. We measured trust and trustworthiness for every individual in an incoming cohort of undergraduate students before they began interacting. Using relationship data sourced from surveys and campus entry/exit times between one month and two years after the trust experiment, we find that reciprocal trust is neither a statistically nor an economically significant factor in determining the students’ social networks. Instead, time of exposure, prior acquaintance, and other demographic characteristics play important and persistent roles in relationship formation.

The Latent Position Model (LPM) is a popular approach for the statistical analysis of network data. A central aspect of this model is that it assigns nodes to random positions in a latent space, such that the probability of an interaction between each pair of individuals or nodes is determined by their distance in this latent space. A key feature of this model is that it allows one to visualize nuanced structures via the latent space representation. The LPM can be further extended to the Latent Position Cluster Model (LPCM), to accommodate the clustering of nodes by assuming that the latent positions are distributed following a finite mixture distribution. In this paper, we extend the LPCM to accommodate missing network data and apply this to non-negative discrete weighted social networks. By treating missing data as “unusual” zero interactions, we propose a combination of the LPCM with the zero-inflated Poisson distribution. Statistical inference is based on a novel partially collapsed Markov chain Monte Carlo algorithm, where a Mixture-of-Finite-Mixtures (MFM) model is adopted to automatically determine the number of clusters and optimal group partitioning. Our algorithm features a truncated absorb-eject move, which is a novel adaptation of an idea commonly used in collapsed samplers, within the context of MFMs. Another aspect of our work is that we illustrate our results on 3-dimensional latent spaces, maintaining clear visualizations while achieving more flexibility than 2-dimensional models. The performance of this approach is illustrated via three carefully designed simulation studies, as well as four different publicly available real networks, where some interesting new perspectives are uncovered.

When undertaking a community intervention, interventionists frequently recruit the help of community members who serve as key opinion leaders (KOLs). However, selecting a team of KOLs can be challenging because the evaluation of potential teams must balance considerations of members’ availability and diversity, as well as the team’s breadth of network coverage and cost of recruitment. This paper has two goals: to review the practical challenges that arise in the selection of KOLs for community interventions, and to facilitate the selection of KOLs when some of these practical challenges are present by introducing and demonstrating the KOLaide R package. We conclude by discussing future directions for facilitating the selection of KOLs in community intervention contexts.

Counting the number of isomers of a chemical molecule is one of the formative problems of graph theory. However, recent progress has been slow, and the problem has largely been ignored in modern network science. Here we provide an introduction to the mathematics of counting network structures and then use it to derive results for two new classes of molecules. In contrast to previously studied examples, these classes take additional chemical complexity into account and thus require the use of multivariate generating functions. The results illustrate the elegance of counting theory, highlighting it as an important tool that should receive more attention in network science.

This paper presents an illustrated tutorial for conducting an embedded Mixed-Method Social Network Analysis (MMSNA) to examine the dynamic interplay between human agency and social networks. We draw on an empirical study in education that investigated how teachers enact relational agency within their school networks to support the integration of migrant students. We propose a replicable method and stepwise procedure for designing, implementing and evaluating an embedded MMSNA. While the potential of MMSNA has long been recognized across disciplines, its purpose and operationalization are often underexplained. We illustrate how MMSNA can be used to analyze both network structures and the agency of actors embedded within them, in alignment with specific research objectives and theoretical perspectives.

Core-periphery (CP) structure is frequently observed in networks where the nodes form two distinct groups: a small, densely interconnected core and a sparse periphery. Borgatti and Everett (Borgatti, S. P., & Everett M. G. (2000). Models of core/periphery structures. Social Networks, 21(4), 375–395.) proposed one of the most popular methods to identify and quantify CP structure by comparing the observed network with an “ideal” CP structure. While this metric has been widely used, an improved algorithm is still needed. In this work, we detail a greedy, label-switching algorithm to identify CP structure that is both fast and accurate. By leveraging a mathematical reformulation of the CP metric, our proposed heuristic offers an order-of-magnitude improvement on the number of operations compared to a naive implementation. We prove that the algorithm monotonically ascends to a local maximum while consistently yielding solutions within 90% of the global optimum on small toy networks. On synthetic networks, our algorithm exhibits superior classification accuracies and run-times compared to a popular competing method, and on one-real- world network, it is 340 times faster.

Understanding the values held by negotiating parties is central to the design and success of international climate change agreements. However, empirical understandings of these values – and the manners by which they structure negotiating countries’ value networks and interactions over time – are severely limited. In addressing this shortcoming, this paper uses keyword-assisted topic models to extract value networks for the 13 most recent Conferences of the Parties (COPs) to the United Nations Framework Convention on Climate Change (UNFCCC). It then uses network analysis tools to unpack these networks in relation to influential values, countries, and time. In doing so, it demonstrates that countries’ core climate change values (i) can be accurately recovered from COP High-level Segment (HLS) speeches and (ii) can, in turn, be used to understand the structure of negotiation networks at the UNFCCC. Analysis of the corresponding value networks for COPs 16–28 indicates that initially central values of “Fairness” and “Power” have increasingly given way to values associated with the “Environment” and “Achievement.” Thus, countries at the UNFCCC have increasingly eschewed values associated with common but differentiated responsibilities in favor of a consensus over the urgency of collectively combating climate change. These and related insights illustrate our approach’s potential for recovering and understanding value networks within climate change negotiations – a critical first step for any successful climate change agreement.

We investigate why conservative online news media are often seen as niche, whereas liberal outlets have ideologically broader audiences. We examine two explanatory mechanisms for this asymmetry. The behavioral explanation focuses on differences in homophily, where one ideological camp would be exposed to more cross-cutting content due to more diverse networking preferences. The structural explanation highlights how a platform’s user base places some in the minority, naturally exposing them to more cross-cutting content. We analyze network exposure and sharing of news media content among 420,000 US Twitter users in 2022, prior to Musk’s acquisition of the platform. We find that conservative users, as the minority, were overexposed to cross-cutting media content through their network contacts, while liberal users, as the majority, were underexposed. Consequently, liberal media were shared across party lines, while conservative media were overlooked by liberals and circulated mostly within a tight network of conservative accounts. This apparent paradox suggests that although conservatives primarily engage with their own media, liberal outlets attract a broader audience, including many conservatives. By combining observational data with simulated benchmarks, we find that the structural mechanism plays a primary role in the observed asymmetry, as exposure to liberal content extends farther into conservative online communities.