Related papers: Hypergraph Motifs and Their Extensions Beyond Bina…

In many real-world scenarios, interactions happen in a group-wise manner with multiple entities, and therefore, hypergraphs are a suitable tool to accurately represent such interactions. Hyperedges in real-world hypergraphs are not composed…

From social to biological systems, many real-world systems are characterized by higher-order, non-dyadic interactions. Such systems are conveniently described by hypergraphs, where hyperedges encode interactions among an arbitrary number of…

Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…

Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…

Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…

Understanding human mobility is essential for applications ranging from urban planning to public health. Traditional mobility models such as flow networks and colocation matrices capture only pairwise interactions between discrete…

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighbourhoods of nodes in hypergraphs. We establish their relationships to lattice…

Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…

Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…

Many processes, from gene interaction in biology to computer networks to social media, can be modeled more precisely as temporal hypergraphs than by regular graphs. This is because hypergraphs generalize graphs by extending edges to connect…

Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering…

Dynamic topic modeling is widely used to analyze evolving trends in scientific literature, medical records, and social media. Traditional topic models represent each topic through a single probability vector on the multinomial simplex and…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically…

In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking…

Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are…

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…

Hypergraphs model higher-order relations that drive real-world decisions, from drug prescriptions to recommendations. A central structural signal in such data, beyond what pairwise relations can express, is interaction compositionality:…