Related papers: Spectral properties of complex networks
We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These…
It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). In \cite{BW10} we demonstrated that it is possible to reduce a network,…
In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an…
Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary…
We introduce a new methodology for model selection in the context of modeling network data. The statistical network analysis literature has developed many different classes of network data models, with notable model classes including…
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…
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…
We propose a method based on the Wang-Landau algorithm to numerically generate the spectral densities of random matrix ensembles. The method employs Dyson's log-gas formalism for random matrix eigenvalues and also enables one to…
We develop a theoretical framework based on the cavity and replica methods to analyze the spectral properties of sparse asymmetric correlation matrices of the form $\boldsymbol{F} = (\boldsymbol{X}\boldsymbol{Y}^\top + \omega…
The spectrum of the adjacency matrix plays several important roles in the mathematical theory of networks and in network data analysis, for example in percolation theory, community detection, centrality measures, and the theory of dynamical…
Many methods have been developed for finding the commonalities between different organisms to study their phylogeny. The structure of metabolic networks also reveal valuable insights into metabolic capacity of species as well as into the…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
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…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the…
A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…
The dynamics of complex networks, being a current hot topic of many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we…
Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection…
We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for…
It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…