Related papers: Spectral analysis of deformed random networks
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…
We analyze the spectral properties of the high-dimensional random geometric graph $G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
We investigate the spectral statistics of an interacting fermionic system derived by projecting the Hubbard interaction onto the two lowest-energy, degenerate flat bands of the dice lattice subjected to a $\pi$-flux. Surprisingly, the…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
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 full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…
Spectral methods based on the eigenvectors of matrices are widely used in the analysis of network data, particularly for community detection and graph partitioning. Standard methods based on the adjacency matrix and related matrices,…
The eigendecomposition of the coupling matrix of large biological networks is central to the study of the dynamics of these networks. For neural networks, this matrix should reflect the topology of the network and conform with Dale's law…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and $p$-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…