Federico Battiston

Alec Kirkley, Helcio Felippe, Federico Malizia et al.

Hypergraphs provide a natural framework for describing complex networked systems with higher-order, non-dyadic interactions. Due to their high dimensionality and often redundant structure, a key challenge is to develop methods that simplify hypergraph representations while preserving the essential structure of interactions. Here we present a principled, efficient, and non-parametric information-theoretic method for pruning nested and/or redundant structures in hypergraphs, enabling a minimal representation of higher-order interactions in the presence of local heterogeneity. Our approach naturally extends to weighted hypergraphs, where higher-order topology and hyperedge weights combine to identify the system's structural backbone. We validate the method on controlled synthetic hypergraphs and apply it to empirical datasets from diverse domains, demonstrating substantial sparsification without loss of core structural information.

Quintino Francesco Lotito, Lorenzo Betti, Berné Nortier et al.

The availability of network datasets advances research in network science, machine learning and related fields by enabling empirical analyses and their reproducibility, algorithm development, model validation and benchmarking. Existing repositories, such as SNAP and Netzschleuder, have made traditional network datasets widely accessible with metadata, metrics, and basic visualizations. However, they primarily focus on pairwise interactions, limiting data access to systems with many-body interactions. To address this gap, we created hypergraphx-data, a repository of real-world hypergraph datasets for higher-order network analysis, spanning different domains from social networks to biology and finance, and supporting configurations such as weighted, directed, temporal, and multiplex hypergraphs. Each dataset includes relational information and metadata, provided in an open JSON format and a binarized format for Hypergraphx. We provide a user-friendly interface to facilitate browsing, filtering, and accessing the datasets, while also ensuring integrity and reproducibility through hash-based verification and data versioning. The repository is available at https://hgx-team.github.io/hypergraphx-data

Jaume Llabrés, Onkar Sadekar, Federico Malizia et al.

Evolutionary game theory has provided substantial contributions to explain the emergence of cooperation under unfavourable conditions in ecology, economics, and the social sciences. Recently, inspired by newly available empirical evidence on group interactions, higher-order networks have emerged as a natural framework to properly encode multiplayer games in structured populations. Here, we study the emergence of cooperation in a nonlinear public goods game (PGG) on hypergraphs, where collective reinforcement captures the synergistic or discounting effect associated with each additional cooperator. In well-mixed populations, single-order PGGs, where all games have the same number of players, display a change in the nature of transition from continuous to discontinuous depending on the exact form of nonlinearity. By contrast, mixed-order PGGs, where games with different number of players coexist, exhibit a richer dynamical regime wherein a state of active coexistence of bistability and cooperation can arise. We further find that scale-free hypergraphs promote cooperation, highlighting the crucial role played by both the initial placement of cooperators and the presence of hyperdegree correlations. Overall, our results provide a comprehensive characterization of nonlinear PGGs on hypergraphs and open up new avenues for richer models of evolutionary dynamics of multiplayer interactions on structured populations.

Stefano Gurciullo, Michael Smallegan, María Pereda et al.

This study is a first, exploratory attempt to use quantitative semantics techniques and topological analysis to analyze systemic patterns arising in a complex political system. In particular, we use a rich data set covering all speeches and debates in the UK House of Commons between 1975 and 2014. By the use of dynamic topic modeling (DTM) and topological data analysis (TDA) we show that both members and parties feature specific roles within the system, consistent over time, and extract global patterns indicating levels of political cohesion. Our results provide a wide array of novel hypotheses about the complex dynamics of political systems, with valuable policy applications.