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.

This is very important to prioritize nodes for immunization in controlling infectious disease outbreaks. In this paper, we propose a new immunization strategy for multiplex networks; we specifically model two separate layers: the physical layer where infection propagates and the virtual layer where information is transmitted. We assume that each layer has a different “context” and use that to identify the most suitable centrality measure for each. For the infection layer, we choose PageRank, as it has shown certain effectiveness in determining those nodes crucial for reducing transmission. For the awareness layer, we show how closeness centrality is a better measure of quality for the passing of information along short paths. We, therefore, propose Multiplex Combined PageRank, or MCPR, combining the centralities from both layers to immunize the most important nodes. The simulations employ the extended SIR-UA model, which exploits the interaction between infection and awareness dynamics, to scenarios on measles and smallpox. Validation on both synthetic networks and the real-world Copenhagen Networks Study dataset demonstrates consistent superiority of MCPR over classical methods. In terms of epidemic size in simulations with very limited immunization budgets, MCPR indeed resulted in better outcomes than the single-layer PageRank immunization strategy and the existing Multiplex PageRank method. Real-world validation shows epidemic size reductions of 2.2% for measles and 7% for smallpox at 10% immunization coverage, with parameter optimization yielding improvements up to 9.5%. The sensitivity analysis demonstrates that increasing transmission of awareness and the quality of information can help control the infection immensely.

Analyses of online social interactions on major platforms have become central to evaluating the ideological leanings of users. Social scientists often represent individuals’ policy preferences as ideal points in a low-dimensional space. We first demonstrate that standard ideal-point estimation approaches can be temporally inconsistent by examining the evolution of ideological positions for political elites and non-elite Twitter users from 2017 to 2022. To address this instability and to improve overall measurement quality, we augment the social-network data conventionally used for ideal-point estimation with unstructured text data widely available on social media. Our results indicate that this data-augmented approach improves identification at the extreme ends of the ideological spectrum and yields robust estimates consistent with those from more complex word-embedding techniques, while offering greater computational efficiency and interpretability. This framework can enhance future studies that measure political ideology using behavioral data and inform broader discussions about integrating textual and network information.

The usual definitions of algorithmic fairness focus on population-level statistics, such as demographic parity or equal opportunity. However, in many social or economic contexts, fairness is not perceived globally, but locally, through an individual’s peer network and comparisons. We propose a theoretical model of perceived fairness networks, in which each individual’s sense of discrimination depends on the local topology of interactions. We show that even if a decision rule satisfies standard criteria of fairness, perceived discrimination can persist or even increase in the presence of homophily or assortative mixing. We propose a formalism for the concept of fairness perception, linking network structure, local observation, and social perception. Analytical and simulation results highlight how network topology affects the divergence between objective fairness and perceived fairness, with implications for algorithmic governance and applications in finance and collaborative insurance.

Personal networks provide crucial support during crises, yet people are embedded in different network types that structure unequal access to such resources. The current study integrates these perspectives to examine whether—and how—network turnover contributed to disparities in mental health across socioeconomic status (SES) groups during the pandemic. Using two-wave panel data from the COVID-19 Pandemic and Social Network Panel Study (2020–2021), an egocentric network study of the college population in Wuhan, we employ random forests and spectral clustering to identify 7 types of core networks based on 43 network variables (i.e., Family, Friend, Restricted, Family & Community, School & Career, Just Activity, and Homebody). We find that as local social-distancing policies tightened, respondents increasingly shifted to Family and Friend networks and withdrew from School & Career and Just Activity. Individual fixed-effect models reveal that these network turnovers have heterogeneous mental health consequences net of observed and time-invariant unobserved confounders. Moving into Family and Friend networks yields the most favorable mental health outcomes for higher-SES groups, whereas benefits are less pronounced and even reversed among lower-SES groups. This pattern is consistent with SES-based differences in social support available in these network types. The current research advances an updated machine-learning approach for identifying personal network typologies. It also shows how the pandemic laid bare unequal resources embedded in personal networks and intensified health-related social inequality, underscoring the need to theorize network effects as contingent on individuals’ social status and the contexts in which networks are formed and embedded.

This article studies latent space models for social network data in which actors are embedded on a hypersphere and link probabilities depend on angular similarity. In contrast to Euclidean embeddings, the spherical formulation provides a compact parameter space, stabilizes the linear predictor through bounded inner products, and offers a natural representation of directional and cyclic structure. For inference, we combine maximum likelihood estimation, used to obtain initial values for latent positions and model parameters, with geometry-aware Bayesian methods based on Metropolis–Hastings and Hamiltonian Monte Carlo algorithms, including a geodesic Hamiltonian scheme for manifold-constrained parameters. We conduct a systematic empirical comparison between Euclidean and spherical latent space models on a benchmark social network dataset, evaluating model fit, predictive performance, and interpretability. The results show that spherical representations provide competitive performance while offering a more constrained and geometrically interpretable structure. Overall, the paper clarifies the role of latent space geometry in network modeling and highlights the importance of geometry-aware inference in statistical analysis of relational data.

Community structure in networks naturally arises in various applications. But while the topic has received significant attention for static networks, the literature on community structure in temporally evolving networks is more scarce. In particular, there are currently no statistical methods available to test for the presence of community structure in a sequence of networks evolving over time. In this work, we propose a simple yet powerful test using e-values, an alternative to p-values that is more flexible in certain ways. Specifically, an e-value framework retains valid testing properties even after combining dependent information, a relevant feature in the context of testing temporal networks. We apply the proposed test to synthetic and real-world networks, demonstrating various features inherited from the e-value formulation and exposing some of the inherent difficulties of testing on temporal networks.

Social network experiments provide a powerful framework for identifying causal network effects but also allow a specific form of network endogeneity. Random assignment eliminates the correlation between individual differences and treatment assignment but not between individual differences and treatment response. Individual differences can shape how participants enact their assigned networks. We use data from three networks to demonstrate an underappreciated approach for estimating causal network effects in the presence of endogeneity. The pre-experiment network captures individual differences, the treatment network defines the assigned structure, and the behavioral network reflects the interactions that occur during the experiment. Because the treatment network is exogenously assigned, it can serve as an instrument for the behavioral network, isolating the causal component of behavioral network effects. Using data from a coordination experiment, we estimate the causal effect of brokerage in the behavioral network on an important team outcome: perceived leadership. We also examine the influence of pre-experiment networks, finding that individuals who enter with closed networks sometimes emerge as brokers. The result shows that behavioral networks form through interdependent choices and interactions among multiple individuals and that endogenous network structures can generate effects beyond the control or intentions of any single individual.

Plant xylem consists of a network of interconnected vessels, through which water is transported under negative pressure. Filling of vessels with air, or embolism, disturbs this transport process and, in extreme cases, leads to tree mortality. Despite this significance, embolism propagation dynamics are still poorly understood, primarily because xylem is opaque to direct observation. Furthermore, existing models of embolism spreading build excessively on physiological and anatomical parameters, and many misrepresent the intervessel pit membrane as a 2D surface. Here, we first extend these physiological models by implementing the pit membrane as a 3D object. Then, we introduce a susceptible-infected (SI) model, a simple stochastic model for tracking spreading through a population, for embolism propagation. After correctly fitting the spreading probability, our SI model reproduces vulnerability curves produced by both the physiological model and empirical data, highlighting that the SI model can address embolism spreading dynamics in plant species, for which detailed physiological data are not available. Furthermore, relating the SI model to the physiological one allows interpreting embolism spreading as a directed percolation process. Elucidating the exact mapping between directed percolation and embolism spreading will likely yield new fundamental insights into the relationships between xylem network architecture and embolism dynamics.

Ethical considerations in social network studies are grounded in the general principles of human subjects’ research, including avoidance of harm, promotion of justice, equitable distribution of burdens and benefits, respect for human dignity, and protection of confidentiality. To help navigate these challenges, this article presents recommendations for conducting ethical network research, developed by a multi-disciplinary and multi-national working group. The article is divided in three main sections where there are certain recommendations identified for each one of them: data collections, use, and availability. Discovering how others addressed and solved problems can be a way for all of us to improve our capacity to stand up to the scrutiny of ethical governance bodies, while also increasing our capacity to responsibly address novel, rare, or otherwise difficult situations for which institutions provide limited guidance. We see this as a first step toward a virtuous circle, or a form of “generalized indirect reciprocity” whereby researchers share information that may be relevant for others, and benefit at the same time from the information given by other members of the social networks analysis community. Our goal is to continue to produce and promote scientifically solid, ethical social network research.

When collecting covert network data, researchers prioritize finding edges without confirming the absence of a tie. This suggests value in research on the process of sampling edges. However, little research has been done in this area. We use the line graph and the auto-logistic actor attribute model to systematically formulate biased sampling processes to reflect realistic sampling biases. We define what might be termed person of interest (POI) bias in the model to reflect the dependence between sampled edges. We present a few examples using different population networks. We conclude that biased sampling processes can result in highly structured observed networks even when the population network lacks structure.

This paper advances a methodological framework for the study of policy polarization. We conceptualize polarization as the structure of relationships among political and epistemic actors, measurable through the similarity of their policy statements. To generate these relational data, large language models (LLMs) are employed as scalable tools for extracting, summarizing, and synthesizing policy statements or positions from diverse textual sources, including debates, party platforms, interviews, and think tank publications. The resulting corpus is embedded into a shared vector space, and similarity measures between statements provide the basis for constructing multimodal networks that connect policy statements through semantic similarity and link them to candidates and think tanks. These networks enable the application of social network analysis, such as correspondence analysis, influence modeling, and structural comparison, to model alignments, divergences, and patterns of polarization. The framework contributes a replicable and extensible approach to analyzing policy polarization, integrating computational text processing with network-analytic models to capture the relational dynamics of political discourse.

The study of polarization in social networks is complicated by conceptual confusion: key forms of polarization include issue, ideological, affective, interactional, interpretive, and perceived polarization, but consensus remains elusive on which of these concepts are most important, how they are interrelated, and whether they should be considered problematic. In this article, we show how the communicative practices of the various actors in a given public debate can be analyzed to reveal the networked structures of discursive alignments and divergences and assess the degree of alliance or opposition between them, and how this analysis in turn provides a basis for the identification of polarization and its potential diagnosis as destructive. We address the challenge of assessing polarization by introducing the new analytical approach of practice mapping. Conceptually supported by practice theory, practice mapping advances beyond conventional social network analysis by no longer grounding its network analysis only in the direct network ties made by participants in social networks, but conceptualizing each participant’s broader patterns of action and interaction within the social network (including their engagement with other participants, but also their information sourcing, language choices, and other qualities of their participation) as that participant’s unique communicative practice—and then constructing and mapping the network of similarities between these practices for all participants. This serves as a key step towards identifying and analyzing patterns of polarization in public discourse. To illustrate this approach, we apply it to public posts on Facebook about the Voice to Parliament referendum in Australia. Our practice mapping was able not only to clearly identify the deeply opposed Yes and No campaigns, but also to show substantial distinctions between the highly centralized and unified No camp and the loose and uncoordinated discursive alliances supporting the Yes camp. Using this case study, we demonstrate the utility of practice mapping in assessing polarization in social networks.