Related papers: Asymptotic theory for the multidimensional random …

We compute an asymptotic expansion in $1/c$ of the limit in $n$ of the empirical spectral measure of the adjacency matrix of an Erd\H{o}s-R\'enyi random graph with $n$ vertices and parameter $c/n$. We present two different methods, one of…

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the…

In this paper, we investigate the energy of a weighted random graph $G_p(f)$ in $G_{n,p}(f)$, in which each edge $ij$ takes the weight $f(d_i,d_j)$, where $d_v$ is a random variable, the degree of vertex $v$ in the random graph $G_p$ of the…

We study the long-time asymptotics of a network of weakly reinforced P\'olya urns. In this system, which extends the WARM introduced by R. van der Hofstad et. al. (2016) to countable networks, the nodes fire at times given by a Poisson…

Consider a random multigraph G* with given vertex degrees d_1,...,d_n, contructed by the configuration model. We show that, asymptotically for a sequence of such multigraphs with the number of edges (d_1+...+d_n)/2 tending to infinity, the…

It is shown that the following holds for each $\varepsilon>0$. For $G$ an $n$-vertex graph of maximum degree $D$ and "lists" $L_v$ ($v \in V(G)$) chosen independently and uniformly from the ($(1+\varepsilon)\ln n$)-subsets of $\{1, ...,…

We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from $\mathbb{Z}^2$ by replacing every edge by a sufficiently large, but fixed number of edges in…

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…

We give the first almost-linear time algorithm for computing the \emph{maximal $k$-edge-connected subgraphs} of an undirected unweighted graph for any constant $k$. More specifically, given an $n$-vertex $m$-edge graph $G=(V,E)$ and a…

We consider the problem of estimating the edge density of densest $K$-node subgraphs of an Erd\"os-R\'{e}nyi graph $\mathbb{G}(n,1/2)$. The problem is well-understood in the regime $K=\Theta(\log n)$ and in the regime $K=\Theta(n)$. In the…

We consider random interlacements on Z^d, with d bigger or equal to 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of…

We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…

We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…

We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…

In this paper, we study some important statistics of the random graph in the directed preferential attachment model introduced by B. Bollob\'as, C. Borgs, J. Chayes and O. Riordan. First, we find a new asymptotic formula for the expectation…

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

We study the critical behavior of inhomogeneous random graphs where edges are present independently but with unequal edge occupation probabilities. The edge probabilities are moderated by vertex weights, and are such that the degree of…

Suppose that under the action of gravity, liquid drains through the unit $d$-cube via a minimal-length network of channels constrained to pass through random sites and to flow with nonnegative component in one of the canonical orthogonal…

Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…