Related papers: Spectra of high-dimensional sparse random geometri…

We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erd\H{o}s-R\'enyi graphs. Our error bounds are sharp for a large class of sparse random matrices.…

We study the spectrum of a random multigraph with a degree sequence ${\bf D}_n=(D_i)_{i=1}^n$ and average degree $1 \ll \omega_n \ll n$, generated by the configuration model, and also the spectrum of the analogous random simple graph. We…

We study the limiting spectral distribution of the normalized Laplacian $\mathcal L$ of an Erd\H{o}s-R\'enyi graph $G(n,p)$. To account for the presence of isolated vertices in the sparse regime, we define $\mathcal L$ using the…

McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large…

In this paper we study the spectrum of the random geometric graph $G(n,r)$, in a regime where the graph is dense and highly connected. In the \erdren $G(n,p)$ random graph it is well known that upon connectivity the spectrum of the…

We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erd\"os-Renyi random graph with $N$ vertices of average degree $Z$, inserting a real symmetric $d \times d$ random block at each non-vanishing…

We consider Erd\H{o}s-R\'enyi-type random hypergraphs that are non-uniform, in the sense that hyperedges of different sizes may coexist, and inhomogeneous, in that connection probabilities may depend on the hyperedge size. All parameters…

In the random geometric graph model $\mathsf{Geo}_d(n,p)$, we identify each of our $n$ vertices with an independently and uniformly sampled vector from the $d$-dimensional unit sphere, and we connect pairs of vertices whose vectors are…

We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the…

We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of…

For any $\alpha\in (0,1)$ and any $n^{\alpha}\leq d\leq n/2$, we show that $\lambda(G)\leq C_\alpha \sqrt{d}$ with probability at least $1-\frac{1}{n}$, where $G$ is the uniform random $d$-regular graph on $n$ vertices, $\lambda(G)$ denotes…

The randomly oriented graph $G_{n,p}^{\sigma}$ is an Erd\H{o}s-R\'enyi random graph $G_{n,p}$ with a random orientation $\sigma$, which assigns to each edge a direction so that $G_{n,p}^{\sigma}$ becomes a directed graph. Denote by $S_n$…

The spectral moments of ensembles of sparse random block matrices are analytically evaluated in the limit of large order. The structure of the sparse matrix corresponds to the Erd\"os-Renyi random graph. The blocks are i.i.d. random…

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…

For a class of sparse random matrices of the form $A_n =(\xi_{i,j}\delta_{i,j})_{i,j=1}^n$, where $\{\xi_{i,j}\}$ are i.i.d.~centered sub-Gaussian random variables of unit variance, and $\{\delta_{i,j}\}$ are i.i.d.~Bernoulli random…

We consider the random geometric graph on $n$ vertices drawn uniformly from a $d$--dimensional sphere. We focus on the sparse regime, when the expected degree is constant independent of $d$ and $n$. We show that, when $d$ is larger than $n$…

We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…

We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar…

We bound the second eigenvalue of random $d$-regular graphs, for a wide range of degrees $d$, using a novel approach based on Fourier analysis. Let $G_{n, d}$ be a uniform random $d$-regular graph on $n$ vertices, and let $\lambda (G_{n,…

We consider the ensemble of adjacency matrices of Erd\H{o}s-R\'{e}nyi random graphs, that is, graphs on $N$ vertices where every edge is chosen independently and with probability $p\equiv p(N)$. We rescale the matrix so that its bulk…