Related papers: Simplicity of random hypergraphs
We prove that any quasirandom uniform hypergraph $H$ can be approximately decomposed into any collection of bounded degree hypergraphs with almost as many edges. In fact, our results also apply to multipartite hypergraphs and even to the…
Consider a random multigraph with given vertex degrees constructed by the configuration model. We give a new proof of the fact that, asymptotically for a sequence of such multigraphs with the number of edges tending to infinity, the…
Graph models have long been used in lieu of real data which can be expensive and hard to come by. A common class of models constructs a matrix of probabilities, and samples an adjacency matrix by flipping a weighted coin for each entry.…
Twisted hypercubes are generalizations of the Boolean hypercube, obtained by iteratively connecting two instances of a graph by a uniformly random perfect matching. Dudek et al. showed that when the two instances are independent, these…
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…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that…
Hypergraphs generalize classical graphs by allowing a single edge to connect multiple vertices, providing a natural language for modeling higher-order interactions. Superhypergraphs extend this paradigm further by accommodating nested,…
High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases…
In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…
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…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…
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…
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…
The threshold model has been widely adopted as a prototype for studying contagion processes on social networks. In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
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…
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…