Related papers: Hypergraph Animals
Psychological network approaches propose to see symptoms or questionnaire items as interconnected nodes, with links between them reflecting pairwise statistical dependencies evaluated cross-sectional, time-series, or panel data. These…
We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the…
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for an edge of size $t$ to belong to the hypergraph depends of a…
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…
Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
This article discusses random hypergraphs with varying hyperedge sizes, admitting large hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size distributions. The main result describes a threshold for the random…
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…
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…
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…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…
Many large, real-world complex networks have rich community structure that a network scientist seeks to understand. These communities may overlap or have intricate internal structure. Extracting communities with particular topological…
Hypergraph offers a framework to depict the multilateral relationships in real-world complex data. Predicting higher-order relationships, i.e hyperedge, becomes a fundamental problem for the full understanding of complicated interactions.…
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…
Complex networks can be used to analyze structures and systems in the embryo. Not only can we characterize growth and the emergence of form, but also differentiation. The process of differentiation from precursor cell populations to…
Hypergraphs offer a generalized framework for capturing high-order relationships between entities and have been widely applied in various domains, including healthcare, social networks, and bioinformatics. Hypergraph neural networks, which…
We generalize a sampling algorithm for lattice animals (connected clusters on a regular lattice) to a Monte Carlo algorithm for `graph animals', i.e. connected subgraphs in arbitrary networks. As with the algorithm in [N. Kashtan et al.,…
Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…