Related papers: Hypergraph modelling of wave scattering to speed-u…

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…

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…

A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…

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…

Hypergraphs provide a powerful framework for modeling complex systems and networks with higher-order interactions beyond simple pairwise relationships. However, graph-based clustering approaches, which focus primarily on pairwise relations,…

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We…

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 are important objects to model ternary or higher-order relations of objects, and have a number of applications in analysing many complex datasets occurring in practice. In this work we study a new heat diffusion process in…

Modeling temporal multimodal data poses significant challenges in classification tasks, particularly in capturing long-range temporal dependencies and intricate cross-modal interactions. Audiovisual data, as a representative example, is…

A hypergraph as a generalization of graphs records higher-order interactions among nodes, yields a more flexible network model, and allows non-linear features for a group of nodes. In this article, we propose a hypergraph echo state network…

People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To…

New network models of complex systems use layers, state nodes, or hyperedges to capture higher-order interactions and dynamics. Simplifying how the higher-order networks change over time or depending on the network model would be easy with…

Many problems such as node classification and link prediction in network data can be solved using graph embeddings. However, it is difficult to use graphs to capture non-binary relations such as communities of nodes. These kinds of complex…

We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple…

We present an innovative framework for traffic dynamics analysis using High-Order Evolving Graphs, designed to improve spatio-temporal representations in autonomous driving contexts. Our approach constructs temporal bidirectional bipartite…

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

When describing complex interconnected systems, one often has to go beyond the standard network description to account for generalized interactions. Here, we establish a unified framework to simplify the stability analysis of cluster…

Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…

Hypergraphs are a generalized data structure of graphs to model higher-order correlations among entities, which have been successfully adopted into various research domains. Meanwhile, HyperGraph Neural Network (HGNN) is currently the…

This paper proposes an optimization-based framework for the analysis of multiperiod directed multihypergraphs aimed at identifying self-amplifying structures that sustain endogenous growth in complex systems. The approach captures the…