Abstract 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.

Abstract 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.

Abstract 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.

Abstract Political polarization is a group phenomenon in which opposing factions, often of unequal size, exhibit asymmetrical influence and behavioral patterns. Within these groups, elites and masses operate under different motivations and levels of influence, challenging simplistic views of polarization. Yet, existing methods for measuring polarization in social networks typically reduce it to a single value, assuming homogeneity in polarization across the entire system. While such approaches confirm the rise of political polarization in many social contexts, they overlook structural complexities that could explain its underlying mechanisms. We propose a method that decomposes existing polarization and alignment measures into distinct components. These components separately capture polarization processes involving elites and masses from opposing groups. Applying this method to Twitter discussions surrounding the 2019 and 2023 Finnish parliamentary elections, we find that (1) opposing groups rarely have a balanced contribution to observed polarization, and (2) while elites strongly contribute to structural polarization and consistently display greater alignment across various topics, the masses, too, have recently experienced a surge in alignment. Our method provides an improved analytical lens through which to view polarization, explicitly recognizing the complexity of and need to account for elite-mass dynamics in polarized environments.

Abstract Course-prerequisite networks (CPNs) are directed acyclic graphs that model complex academic curricula by representing courses as nodes and dependencies between them as directed links. These networks are indispensable tools for visualizing, studying, and understanding curricula. For example, CPNs can be used to detect important courses, improve advising, guide curriculum design, analyze graduation time distributions, and quantify the strength of knowledge flow between different university departments. However, most CPN analyses to date have focused only on micro- and meso-scale properties. To fill this gap, we define and study three new global CPN measures: breadth, depth, and flux. All three measures are invariant under transitive reduction and are based on the concept of topological stratification, which generalizes topological ordering in directed acyclic graphs. These measures can be used for macro-scale comparison of different CPNs. We illustrate the new measures numerically by applying them to three real and synthetic CPNs from three universities: the Cyprus University of Technology, the California Institute of Technology, and Johns Hopkins University. The CPN data analyzed in this paper are publicly available in a GitHub repository.

Abstract In many contexts, an individual’s beliefs and behavior are affected by the choices of their social or geographic neighbors. This influence results in local correlation in people’s actions, which in turn affects how information and behaviors spread. Previously developed frameworks capture local social influence using network games, but discard local correlation in players’ strategies. This paper develops a network games framework that allows for local correlation in players’ strategies by incorporating a richer partial information structure than previous models. Using this framework we also examine the dependence of equilibrium outcomes on network clustering—the probability that two individuals with a mutual neighbor are connected to each other. We find that clustering reduces the number of players needed to provide a public good and allows for market sharing in technology standards competitions.

Abstract Networks describe complex relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a data set well, and will extrapolate to similar data. We use recent results in random matrix theory to derive a general goodness-of-fit (GoF) test for dyadic data. We show that our method, when applied to a specific model of interest, provides a straightforward, computationally fast way of selecting parameters in a number of commonly used network models. For example, we show how to select the dimension of the latent space in latent space models. Unlike other network GoF methods, our general approach does not require simulating from a candidate parametric model, which can be cumbersome with large graphs, and eliminates the need to choose a particular set of statistics on the graph for comparison. It also allows us to perform GoF tests on partial network data, such as Aggregated Relational Data. We show with simulations that our method performs well in many situations of interest. We analyze several empirically relevant networks and show that our method leads to improved community detection algorithms.

Abstract Belief network analysis (BNA) has enabled major advances in the study of belief systems, capturing Converse’s understanding of the interdependence among multiple beliefs (i.e., constraint) more intuitively than many conventional statistics. However, BNA struggles with representing political divisions that follow a spatial logic, such as the “left–right” or “liberal-conservative” ideological divide. We argue that Response Item Networks (ResINs) have important advantages for modeling political cleavage lines as they organically capture belief systems in a latent ideological space. In addition to retaining many desirable properties inherent to BNA, ResIN can uncover ideological polarization in a visually intuitive, theoretically grounded, and statistically robust fashion. We demonstrate the advantages of ResIN by analyzing ideological polarization with regard to five hot-button issues from 2000 to 2020 using the American National Election Studies (ANES), and by comparing it against an equivalent procedure using BNA. We further introduce system-level and attitude-level polarization measures afforded by ResIN and discuss their potential to enrich the analysis of ideological polarization. Our analysis shows that ResIN allows us to observe much more detailed dynamics of polarization than classic BNA approaches.

Abstract This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon itself can be viewed more broadly as local density or intensity function on networks, making the model a natural choice for comparison purposes. More precisely, to gain information about the (dis-)similarity between networks, we extend graphon estimation towards modeling multiple networks simultaneously. In particular, fitting a single model implies aligning different networks with respect to the same graphon estimate. To do so, we employ an EM-type algorithm. Drawing on this network alignment consequently allows a comparison of the edge density at local level. Based on that, we construct a chi-squared-type test on equivalence of network structures. Simulation studies and real-world examples support the applicability of our network comparison strategy.

Abstract The main goal of this paper is to introduce a new model of evolvement of beliefs on networks. It generalizes the DeGroot model and describes the iterative process of establishing the consensus in isolated social networks in the case of nonlinear aggregation functions. Our main tools come from mean theory and graph theory. The case, when the root set of the network (influencers, news agencies, etc.) is ergodic is fully discussed. The other possibility, when the root contains more than one component, is partially discussed and it could be a motivation for further research.