Related papers: Spacing ratio statistics of multiplex directed net…
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…
This paper examines the relationship between sparse random network architectures and neural network stability by examining the eigenvalue spectral distribution. Specifically, we generalise classical eigenspectral results to sparse…
Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer…
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
The spectral statistics of non-Hermitian random matrices are of importance as a diagnostic tool for chaotic behavior in open quantum systems. Here, we investigate the statistical properties of singular values in non-Hermitian random…
Algebraic connectivity, the second eigenvalue of the Laplacian matrix, is a measure of node and link connectivity on networks. When studying interconnected networks it is useful to consider a multiplex model, where the component networks…
Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their…
Network epidemic simulation holds the promise of enabling fine-grained understanding of epidemic behavior, beyond that which is possible with coarse-grained compartmental models. Key inputs to these epidemic simulations are the networks…
We study the stochastic susceptible-infected-susceptible model of epidemic processes on finite directed and weighted networks with arbitrary structure. We present a new lower bound on the exponential rate at which the probabilities of nodes…
The directed network of telephone subscribers is considered in the article. It can be described as a dynamic network with vertices that correspond to the subscribers of the telephone network and emerging directional edges that correspond to…
It is becoming increasingly common to see large collections of network data objects -- that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based…
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the…
Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the…
Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors…
We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…
Achieving consensus via nearest neighbor rules is an important prerequisite for multi-agent networks to accomplish collective tasks. A common assumption in consensus setup is that each agent interacts with all its neighbors. This paper…