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Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations…

Adaptation and Self-Organizing Systems · Physics 2023-03-24 Yuanzhao Zhang , Maxime Lucas , Federico Battiston

Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…

Physics and Society · Physics 2021-09-23 Hanlin Sun , Ginestra Bianconi

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

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Social and Information Networks · Computer Science 2025-05-29 John Hood , Caterina De Bacco , Aaron Schein

Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or…

Physics and Society · Physics 2023-09-25 István Z. Kiss , Iacopo Iacopini , Péter L. Simon , Nicos Georgiou

Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…

Physics and Society · Physics 2025-06-06 Junhap Bian , Tao Zhou , Yilin Bi

The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution…

Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…

Physics and Society · Physics 2025-07-22 Nicholas W. Landry , Jean-Gabriel Young , Nicole Eikmeier

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

Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a…

Physics and Society · Physics 2024-02-16 Nicholas W. Landry , Ilya Amburg , Mirah Shi , Sinan G. Aksoy

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…

Social and Information Networks · Computer Science 2018-12-13 Austin R. Benson , Rediet Abebe , Michael T. Schaub , Ali Jadbabaie , Jon Kleinberg

The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks to the establishment of generative models recovering their…

The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems. In our work, we investigate the relationship between higher-order…

Simplicial complex (SC) representation is an elegant mathematical framework for representing the effect of complexes or groups with higher-order interactions in a variety of complex systems ranging from brain networks to social…

Physics and Society · Physics 2021-05-12 Yongsun Lee , Jongshin Lee , Soo Min Oh , Deokjae Lee , B. Kahng

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

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…

Physics and Society · Physics 2023-03-17 Luca Gallo , Lucas Lacasa , Vito Latora , Federico Battiston

Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…

Physics and Society · Physics 2025-12-23 Xiaochen Wang , Lei Zhou , Alex McAvoy , Zhenglong Tian , Aming Li

Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…

Applications · Statistics 2026-03-31 Catherine Matias
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