The Diverse top-k-pc problem is introduced, which is the first principled formulation of top-k polarized communities with controlled overlap, and a greedy sequential algorithm that solves a generalized eigenvector problem at each step, efficiently discovering diverse polarized pairs.
Abstract
Polarization is common in social systems, where individuals tend to form cohesive groups that oppose each other. Signed networks, with positive edges representing agreement and negative edges representing disagreement, provide a natural model for studying such dynamics. The 2-Polarized-Communities problem (2pc) was recently introduced to detect a single pair of polarized communities by maximizing a Rayleigh quotient that balances intra-community agreement and inter-community disagreement. However, real signed networks usually host multiple, coexisting axes of conflict, often with communities that overlap. Existing extension of 2pc to multiple communities or find-and-remove heuristics, either rely on the restrictive assumption that every polarized community is in conflict with all the others, or enforce disjoint solutions–thus failing to capture the nuanced structures observed in real networks. In this paper, we introduce the Diverse top-k-pc problem, which is the first principled formulation of top-k polarized communities with controlled overlap. Our formulation extends the 2pc polarity objective by incorporating diversity terms directly into the denominator of the Rayleigh quotient, yielding a generalized objective that jointly promotes polarity and diversity. We design a greedy sequential algorithm that solves a generalized eigenvector problem at each step, efficiently discovering diverse polarized pairs. Experiments on both real-world and synthetic signed networks demonstrate that our approach identifies multiple meaningful and overlapping pairs of polarized communities, outperforming natural baselines while scaling to large graphs.
Opinion polarization, echo chambers, and the rapid formation of opinion clusters have become defining features of debates on contemporary online social platforms. To explain these phenomena from a control-theoretic perspective, this paper investigates opinion dynamics in social networks with edge-heterogeneous confidence bounds, focusing on clustering and polarization behaviors driven by pair-dependent trust and asymmetric influence. Two discrete-time models are proposed, including an unsigned bounded-confidence model and a more general signed model that incorporates both supportive and oppositional interactions. The interaction structures are described by time-varying unsigned and signed digraphs, respectively, in which heterogeneous interpersonal influence is characterized by edge-dependent confidence bounds that naturally encode platform-mediated trust. For the proposed models, rigorous sufficient conditions are established for invariant cluster consensus and structurally balanced polarization. Numerical simulations, including a case study on the Slashdot Zoo signed social network with 50 controversial users, illustrate the theoretical results and demonstrate their relevance for understanding opinion evolution on internet-scale platforms.
Zumei Huang, Zhuangzhuang Ma, Lei Shi et al.· Future Internet· 0 citations
Homophily, the tendency of individuals to interact with similar others, is key to understand social dynamics. This concept has traditionally been measured in a k-uniform hypergraph model that accounts group interactions involving exactly k individuals (k ≥ 2). However, real-world interactions do not always involve the same number of individuals. Thus, in this paper, we propose a new descriptive homophily measure for general social hypergraphs where group interactions involve arbitrary number of individuals. We establish constraints of monotonic and majority homophily for two-class labels, providing a framework for analyzing homophily patterns. Experiments on several datasets reveal systematic deviations in hyperedge composition associated with node class labels relative to a label-independent baseline, offering insights into homophily pattern in complex social networks. This work bridges the gap between theoretical measures and practical applications in non-uniform hypergraphs, advancing the understanding of social and structural dynamics.
Yunping Wang, Zhiheng Zhou, Mingwei Li et al.· Chaos· 0 citations
Many real-world networks have the characteristic that they are comprised of distinct groups or communities whose members contain many links within the community but with fewer connections to others. It is important to accurately model these types of networks to correctly predict the outcome of important spreading processes such as disease transmission, or the flow of information etc. Our motivating example is a network of traders within several investment institutions such as hedge funds. We assume an idealised scenario where traders within the same institution have many contacts and can share information quickly and easily but have fewer contacts to traders in other institutions, relying on personal networks, allowing for information to flow easily within a community and less-so between communities. In this paper we investigate a particular spreading process, the spread of a rumour, on a community based network that is characterised by two parameters; the within-group connectivity, and the between-group connectivity. We show that such networks have different characteristics to small-world or random networks that are often used to model the types of systems and that the network topology has a small but not insignificant effect on the spread of rumours on the network.
Large language models enable the creation of autonomous agents that interact in social environments, raising the question of whether agent-based platforms reproduce the organizational properties of human social networks. We compare Moltbook, a social network populated by AI agents, with early Reddit, focusing on how communities organize and differentiate semantic content, using network analysis and NLP methods to characterize semantic coherence and diversity within and between communities, and their relationship to user activity. We find a systematic difference between the two platforms. Reddit communities show stronger semantic coherence, closer alignment with community names, and greater semantic diversity, with individual communities spanning broader content and communities more differentiated from one another. This combination distinguishes Reddit from Moltbook, whose communities are more homogeneous, less differentiated, and increasingly misaligned with their names over time. Users on Reddit also participate across communities that are more semantically related than those connected by activity in Moltbook. At the interaction level, comment-network motif analysis shows Moltbook dominated by non-reciprocal, broadcast-like exchanges, whereas Reddit shows more reciprocal, chained interaction patterns. These results indicate that Reddit combines semantic coherence with diversity across organizational levels, a pattern not reproduced by the AI-agent network.
Favio Di Ciocco, L. Celauro, Sebastián Pinto et al.· 0 citations
This paper develops a mean-field framework for modelling opinion polarization and correlated opinion alignment in online communities, with particular attention to the structural conditions under which misinformation-prone environments arise. Rather than tracking the propagation of specific false content, the framework identifies the interaction regimes in which a platform’s aggregation mechanism becomes structurally unable to recover an accurate global opinion signal, which is the condition under which misinformation becomes consequential. We consider a population divided into interacting groups, where individuals hold binary opinions and influence one another through a coupling matrix that captures both within-community and cross-community interactions. Using ideas from statistical mechanics, the model describes collective opinion formation through an energy-based formulation and an associated Gibbs measure. We study the behaviour of the system in the limit of large populations and analyse the resulting community-level opinion margins. Optimal aggregation weights are derived by minimizing the expected discrepancy between the true global opinion and its approximation based on community-level signals. The analysis identifies three regimes of behaviour: weak coupling, the critical regime, and strong coupling, each leading to different macroscopic outcomes. In the weak-coupling regime, opinions are only weakly correlated, and the optimal weights are uniquely determined by a linear system involving the correlation structure. In the strong-coupling regime, the system exhibits either collective alignment or complete polarization, and the optimal weights are no longer uniquely defined. We also distinguish between cooperative and antagonistic interaction structures and show how they lead to consensus formation, echo chambers, or polarized states. These results show how the strength and sign of inter-community coupling determine whether platforms converge toward consensus, fragment into echo chambers, or become irreducibly polarized, and how the resulting aggregation breakdown, in turn, creates the structural conditions under which misinformation thrives.
Richard Kwame Ansah, Richard Kena Boadi, K. Tawiah et al.· Journal of Statistical Mecha...· 0 citations
We study majority correctness when voting is preceded by sustained social interaction on a social network. Motivated by the Condorcet Jury Theorem, we consider a binary choice with an objectively correct alternative, where uninformed voters revise their vote intentions through repeated interaction in the presence of competing committed leaders (zealots). In this zealot--contrarian voter model, voters may either imitate or oppose the views they encounter. For fully mixed electorates, we characterize the long-run distribution of votes and the correlation structure induced among voters, and we show that Erd\H{o}s--R\'enyi networks exhibit the same majority-correctness behavior after an appropriate rescaling of leader influence. Building on these results, we establish a finite-electorate Condorcet-type guarantee: when post-deliberation individual correctness exceeds random choice, a strict majority is more likely to select the correct alternative than a randomly chosen voter. At the same time, we identify an aggregation failure: social interaction can reduce majority accuracy relative to a no-deliberation benchmark in which voters respond only to zealots. As the electorate size tends to infinity, this finite-electorate advantage disappears unless social updating is purely conformist, revealing a tipping point at full conformity: any persistent contrarian updating drives both individual and majority correctness to the random choice level of one half. Simulations on scale-free, ring, and small-world networks further show that topology matters because it shapes the vote correlations generated by social influence: hub-dominated structures generate stronger positive correlations and lower majority accuracy, whereas spatially structured networks generate weaker correlations, preserve a larger effective number of independent judgments, and improve majority accuracy.
