Related papers: Eigenvalues of random graphs with cycles
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…
The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph $G$, is denoted by $q(G)$. Using other parameters related to $G$, bounds for $q(G)$ are proven and then applied to deduce…
We investigate the spectrum of the non-backtracking matrix of a graph. In particular, we show how to obtain eigenvectors of the non-backtracking matrix in terms of eigenvectors of a smaller matrix. Furthermore, we find an expression for the…
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…
The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…
Let $G$ be a graph with $n$ vertices and $\lambda_n(G)$ be the least eigenvalue of its adjacency matrix of $G$. In this paper, we give sharp bounds on the least eigenvalue of graphs without given pathes or cycles and determine the extremal…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
We consider a setting where individuals interact in a network, each choosing actions which optimize utility as a function of neighbors' actions. A central authority aiming to maximize social welfare at equilibrium can intervene by paying…
We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…
We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…
The largest eigenvalue of the adjacency matrix of the networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
Consider the random matrix obtained from the adjacency matrix of a random d-regular graph by multiplying every entry by a random sign. The largest eigenvalue converges, after proper scaling, to the Tracy--Widom distribution.
The extreme eigenvalues of adjacency matrices are important indicators on the influences of topological structures to collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
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…