Related papers: Random Recursive Hypergraphs
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…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
For $n\geq 3$, let $r=r(n)\geq 3$ be an integer. A hypergraph is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if two edges intersect in at most one vertex. In this paper, the number of linear $r$-uniform…
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some…
Recent work in graph models has found that probabilistic hyperedge replacement grammars (HRGs) can be extracted from graphs and used to generate new random graphs with graph properties and substructures close to the original. In this paper,…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
Let $r\ge 3$ be a fixed constant and let $ {\mathcal H}$ be an $r$-uniform, $D$-regular hypergraph on $N$ vertices. Assume further that $ D > N^\varepsilon $ for some $ \varepsilon>0 $. Consider the random greedy algorithm for forming an…
We consider random walks on edge coloured random graphs, where the colour of an edge reflects the cost of using it. In the simplest instance, the edges are coloured red or blue. Blue edges are free to use, whereas red edges incur a unit…
We consider Stanley--Reisner rings $k[x_1,...,x_n]/I(\mc{H})$ where $I(\mc{H})$ is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hypergraphs that are natural generalizations of graphs that…
We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving…
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…
Let $k\geq 2$ and fix a $k$-uniform hypergraph $\mathcal{F}$. Consider the random process that, starting from a $k$-uniform hypergraph $\mathcal{H}$ on $n$ vertices, repeatedly deletes the edges of a copy of $\mathcal{F}$ chosen uniformly…