Related papers: How Do Hyperedges Overlap in Real-World Hypergraph…

This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and…

Complex networked systems in fields such as physics, biology, and social sciences often involve interactions that extend beyond simple pairwise ones. Hypergraphs serve as powerful modeling tools for describing and analyzing the intricate…

Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…

Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…

Graph representations of solid state materials that encode only interatomic distance lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here we propose a hypergraph…

Real-world complex networks are usually being modeled as graphs. The concept of graphs assumes that the relations within the network are binary (for instance, between pairs of nodes); however, this is not always true for many real-life…

Recently, researchers have extended the concept of matchings to the more general problem of finding $b$-matchings in hypergraphs broadening the scope of potential applications and challenges. The concept of $b$-matchings, where $b$ is a…

Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing…

We consider hypergraph visualizations that represent vertices as points in the plane and hyperedges as curves passing through the points of their incident vertices. Specifically, we consider several different variants of this problem by (a)…

Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…

Given a set of finite words, the Overlap Graph (OG) is a complete weighted digraph where each word is a node and where the weight of an arc equals the length of the longest overlap of one word onto the other (Overlap is an asymmetric…

Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…

We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which…

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…

Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…

Real-world graphs are typically complex, exhibiting heterogeneity in the global structure, as well as strong heterophily within local neighborhoods. While a growing body of literature has revealed the limitations of common graph neural…

Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…

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…

Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…