Related papers: An eigenvalue localization theorem for stochastic …
Eigenvector centrality is a linear algebra based graph invariant used in various rating systems such as webpage ratings for search engines. A generalization of the eigenvector centrality invariant is defined which is motivated by the need…
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology…
The randomized singular value decomposition proposed in [27] has certainly become one of the most well-established randomization-based algorithms in numerical linear algebra. The key ingredient of the entire procedure is the computation of…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erd{\H o}s-R{\'e}nyi graph $G(N,p)$. Recently, it was shown by Lee, up to an…
We completely determine the spectrum of an $I$-graph, that is, the eigenvalues of its adjacency matrix. We apply our result to prove known characterizations of connectedness and bipartiteness in $I$-graphs by using an spectral approach.…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
An eigenvalue of a graph $G$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected tricyclic graphs with exactly two main eigenvalues are determined.
An eigenvalue of a graph $G$ is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected tricyclic graphs with exactly two main eigenvalues are determined.
In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…
Large H-selfadjoint random matrices are considered. The matrix $H$ is assumed to have one negative eigenvalue, hence the matrix in question has precisely one eigenvalue of nonpositive type. It is showed that this eigenvalue converges in…
Many tools from the field of graph signal processing exploit knowledge of the underlying graph's structure (e.g., as encoded in the Laplacian matrix) to process signals on the graph. Therefore, in the case when no graph is available, graph…
We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…
A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…
A vertex $v \in V(G)$ is called $\lambda$-main if it belongs to a star set $X \subset V(G)$ of the eigenvalue $\lambda$ of a graph $G$ and this eigenvalue is main for the graph obtained from $G$ by deleting all the vertices in $X \setminus…
The main result of the note describes certain optimal-score partitions, which can be interpreted as optimal resource allocations. This result is based on the fact that any nonnegative square matrix whose column sums are the same as the…
We study the universality of the eigenvalue statistics of the covariance matrices $\frac{1}{n}M^* M$ where $M$ is a large $p\times n$ matrix obeying condition $\bf{C1}$. In particular, as an application, we prove a variant of universality…
It is well known that a family of $n\times n$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the $n$ joint eigenvalues of the family. In…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…