Related papers: Graphs are maximally expressive for higher-order i…

We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…

Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…

Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…

Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…

Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

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…

Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real…

The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…

Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…

Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent…

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…

Graphs depict pairwise relationships between objects within a system. Higher-order interactions (HOIs), which involve more than two objects simultaneously, are common in nature. Such interactions can change the stability of a complex…

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, 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…

Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements…

Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…