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Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…

Social and Information Networks · Computer Science 2018-02-21 Austin R. Benson

Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…

Social and Information Networks · Computer Science 2025-11-27 Kazuki Nakajima , Yuya Sasaki , Takeaki Uno , Masaki Aida

Traditionally, interaction systems have been described as networks, where links encode information on the pairwise influences among the nodes. Yet, in many systems, interactions take place in larger groups. Recent work has shown that…

Adaptation and Self-Organizing Systems · Physics 2020-09-30 Maxime Lucas , Giulia Cencetti , Federico Battiston

Recent research has focused on understanding how cooperation is fostered through various mechanisms in cognitive settings, particularly through pairwise interactions. However, real-world interactions often extend beyond simple dyads,…

Physics and Society · Physics 2024-07-16 Yin-Jie Ma , Zhi-Qiang Jiang , Fan-Shu Fang , Matjaz Perc , Stefano Boccaletti

The most fundamental social interactions among humans occur face to face. Their features have been extensively studied in recent years, owing to the availability of high-resolution data on individuals' proximity. Mathematical models based…

Physics and Society · Physics 2024-06-10 Luca Gallo , Chiara Zappalà , Fariba Karimi , Federico Battiston

Large animal groups -- bird flocks, fish schools, insect swarms -- are often assumed to form by gradual aggregation of sparsely distributed individuals. Using a mathematically precise framework based on time-varying directed interaction…

Populations and Evolution · Quantitative Biology 2025-12-02 Jidong Jin

Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperlinks) of different sizes to the overall network structure. Yet,…

Physics and Society · Physics 2025-08-26 Alberto Ceria , Frank W. Takes

A social interaction (so-called higher-order event/interaction) can be regarded as the activation of the hyperlink among the corresponding individuals. Social interactions can be, thus, represented as higher-order temporal networks, that…

Physics and Society · Physics 2024-08-12 H. A. Bart Peters , Alberto Ceria , Huijuan Wang

Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion…

Physics and Society · Physics 2021-03-15 Iacopo Iacopini , Giovanni Petri , Alain Barrat , Vito Latora

Collective cooperation drives the dynamics of many natural, social, and economic phenomena, making understanding the evolution of cooperation with evolutionary game theory a central question of modern science. Although human interactions…

Physics and Society · Physics 2024-04-12 Yao Meng , Alex McAvoy , Aming Li

Knowledge silos emerge when structural properties of organizational interaction networks limit the diffusion of information. These structural barriers are known to take many forms at different scales - hubs in otherwise sparse…

Physics and Society · Physics 2022-03-03 Laurent Hébert-Dufresne , Guillaume St-Onge , John Meluso , James Bagrow , Antoine Allard

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…

Physics and Society · Physics 2023-03-01 Andrea Santoro , Federico Battiston , Giovanni Petri , Enrico Amico

Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly…

Physics and Society · Physics 2021-10-04 Sandeep Chowdhary , Aanjaneya Kumar , Giulia Cencetti , Iacopo Iacopini , Federico Battiston

Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…

Populations and Evolution · Quantitative Biology 2025-10-07 Marc Duran-Sala , Sandro Meloni , Violeta Calleja-Solanas

Collective behavior is commonly attributed to direct interactions among system components. Using a minimal stochastic model, we show that higher-order collective structure can instead emerge from shared stochastic environments, even in the…

There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a…

Populations and Evolution · Quantitative Biology 2026-02-16 Sean P. Maley , Carlos Gershenson , Stuart A. Kauffman

We study a self-consistent approach to introduce higher-order effects in a branching process model of complex contagion on clustered networks. Branching processes operate over an infinite population such that they never circle back and…

Physics and Society · Physics 2025-11-20 Leah A. Keating , Laurent Hébert-Dufresne

Teams are the fundamental units propelling innovation and advancing modern science. A rich literature links the fundamental features of teams, such as their size and diversity, to academic success. However, such analyses fail to capture…

Physics and Society · Physics 2024-07-18 Sandeep Chowdhary , Luca Gallo , Federico Musciotto , Federico Battiston

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

Social and Information Networks · Computer Science 2023-10-25 Nicolò Ruggeri , Martina Contisciani , Federico Battiston , Caterina De Bacco

A social-ecological network is a formal representation of a corresponding social-ecological system, and encodes a relation within a given system as an interaction. Conventionally, such networks have been defined as encoding and representing…

Algebraic Topology · Mathematics 2022-02-17 Sudeepto Bhattacharya