Related papers: On the pre- and post-positional semi-random graph …
In this paper, we establish the partial correlation graph for multivariate continuous-time stochastic processes, assuming only that the underlying process is stationary and mean-square continuous with expectation zero and spectral density…
A simple undirected graph is said to be {\em semisymmetric} if it is regular and edge-transitive but not vertex-transitive. Every semisymmetric graph is a bipartite graph with two parts of equal size. It was proved in [{\em J. Combin.…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Let $k$ be an integer with $k\geq 2$. A digraph $D$ is $k$-quasi-transitive, if for any path $x_0x_1\ldots x_k$ of length $k$, $x_0$ and $x_k$ are adjacent. Suppose that there exists a path of length at least $k+2$ in $D$. Let $P$ be a…
We investigate the threshold probability for connectivity of sparse graphs under weak assumptions. As a corollary this completely solve the problem for Cartesian powers of arbitrary graphs. In detail, let $G$ be a connected graph on $k$…
The pre-training on the graph neural network model can learn the general features of large-scale networks or networks of the same type by self-supervised methods, which allows the model to work even when node labels are missing. However,…
Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…
We examine two fundamental tasks associated with graph representation learning: link prediction and semi-supervised node classification. We present a novel autoencoder architecture capable of learning a joint representation of both local…
We address the problem of semi-supervised learning in relational networks, networks in which nodes are entities and links are the relationships or interactions between them. Typically this problem is confounded with the problem of…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
We consider graph classes $\mathcal G$ in which every graph has components in a class $\mathcal{C}$ of connected graphs. We provide a framework for the asymptotic study of $\lvert\mathcal{G}_{n,N}\rvert$, the number of graphs in…
Random key graphs represent topologies of secure wireless sensor networks that apply the seminal Eschenauer-Gligor random key predistribution scheme to secure communication between sensors. These graphs have received much attention and also…
Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce "graph-based…
We take a general approach to uncertainty on product spaces, and give sufficient conditions for the independence structures of uncertainty measures to satisfy graphoid properties. Since these conditions are arguably more intuitive than some…
We develop a general procedure that finds recursions for statistics counting isomorphic copies of a graph $G_0$ in the common random graph models ${\cal G}(n,m)$ and ${\cal G}(n,p)$. Our results apply when the average degrees of the random…
It is shown explicitly how self-similar graphs can be obtained as `blow-up' constructions of finite cell graphs $\hat C$. This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals. For a…
We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally…
We consider a random geometric graph process where random points $(X_i)_{i \ge 1}$ are embedded consecutively in the $d$-dimensional unit torus $\mathbb{T}^d$, and every two points at distance at most $r$ form an edge. As $r\to 0$, we…
We consider a number $\nu_n$ of components in a random graph $G(n,p)$ with $n$ vertices, where the probability of an edge is equal to $p$. By operating with special generating functions we shows the next asymptotic relation for factorial…