Related papers: Connectivity for random graphs from a weighted bri…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
We consider the following question. We have a dense regular graph $G$ with degree $\alpha n$, where $\alpha>0$ is a constant. We add $m=o(n^2)$ random edges. The edges of the augmented graph $G(m)$ are given independent edge weights $X(e)$,…
Consider the complete n-vertex graph whose edge-lengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along the shortest path. Each edge gets some…
Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
We consider the graphs whose edges are marked by the integers (weights) from $0$ to $q-1$ (zero corresponds to no-edge). Such graph is called additive if its vertices can be marked in such a way that the weight of every edge is equal to the…
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 number of crossings in a graph which is embedded randomly on a convex set of points. We give an estimate to the normal distribution in Kolmogorov distance which implies a convergence rate of order $n^{-1/2}$ for various…
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…
Consider a graph on $n$ uniform random points in the unit square, each pair being connected by an edge with probability $p$ if the inter-point distance is at most $r$. We show that as $n\to\infty$ the probability of full connectivity is…
We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertex-edge random graphs. Edge random graphs are Erdos-Renyi random graphs, vertex random graphs are generalizations of geometric random graphs, and…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…