Related papers: Eigenvalue spectra and stability of directed compl…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
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…
The largest eigenvalue of a network's adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically…
A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often such spectral…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
The eigenvalue spectrum of the adjacency matrix of a network is closely related to the behavior of many dynamical processes run over the network. In the field of robotics, this spectrum has important implications in many problems that…
This paper focuses on large neural networks whose synaptic connectivity matrices are randomly chosen from certain random matrix ensembles. The dynamics of these networks can be characterized by the eigenvalue spectra of their connectivity…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
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…
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…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
We provide a general formula for the eigenvalue density of large random $N\times N$ matrices of the form $A = M + LJR$, where $M$, $L$ and $R$ are arbitrary deterministic matrices and $J$ is a random matrix of zero-mean independent and…
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…