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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…
The semirandom graph process constructs a graph $G$ in a series of rounds, starting with the empty graph on $n$ vertices. In each round, a player is offered a vertex $v$ chosen uniformly at random, and chooses an edge on $v$ to add to $G$.…
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…
Random geometric graphs result from taking $n$ uniformly distributed points in the unit cube, $[0,1]^d$, and connecting two points if their Euclidean distance is at most $r$, for some prescribed $r$. We show that monotone properties for…
The vertex-random graphs called proximity catch digraphs (PCDs) have been introduced recently and have applications in pattern recognition and spatial pattern analysis. A PCD is a random directed graph (i.e., digraph) which is constructed…
Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within…
Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art…
We analyze the asymptotic number and typical structure of claw-free graphs at constant edge densities. The first of our main results is a formula for the asymptotics of the logarithm of the number of claw-free graphs of edge density $\gamma…
In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes. While learning arbitrary graphs with $n$ nodes and…
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent…
In this paper we prove discrete to continuum convergence rates for Poisson Learning, a graph-based semi-supervised learning algorithm that is based on solving the graph Poisson equation with a source term consisting of a linear combination…
We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away points are less likely to be connected than nearby points. We…
We prove that the local limit of the weighted spanning trees on any simple connected high degree almost regular sequence of electric networks is the Poisson(1) branching process conditioned to survive forever, by generalizing [NP22] and…
Consider a stationary Poisson process in a $d$-dimensional hyperbolic space. For $R>0$ define the point process $\xi_R^{(k)}$ of exceedance heights over a suitable threshold of the hyperbolic volumes of $k$th nearest neighbour balls centred…
We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…
We consider the contact process on a dynamic graph defined as a random $d$-regular graph with a stationary edge-switching dynamics. In this graph dynamics, independently of the contact process state, each pair $\{e_1,e_2\}$ of edges of the…
We investigate random processes for generating task-dependency graphs of order $n$ with $m$ edges and a specified number of initial vertices and terminal vertices. In order to do so, we consider two random processes for generating…
We investigate the extremal properties of saturated partial plane embeddings of maximal planar graphs. For a planar graph $G$, the plane-saturation number $\mathrm{sat}_{\mathcal{P}}(G)$ denotes the minimum number of edges in a plane…
We consider random graphs $\mathcal{G}$ built on a homogeneous Poisson point process on $\mathbb{R}^d$, $d\geq 2$, with points $x$ marked by i.i.d. random variables $E_x$. Fixed a symmetric function $h(\cdot, \cdot)$, the vertexes of…
The planted densest subgraph detection problem refers to the task of testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $n$ vertices. Under…