Related papers: Eigenvalue spectra and stability of directed compl…
It is well-known that the behavior of many dynamical processes running on networks is intimately related to the eigenvalue spectrum of the network. In this paper, we address the problem of inferring global information regarding the…
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…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
Complex networks with directed, local interactions are ubiquitous in nature, and often occur with probabilistic connections due to both intrinsic stochasticity and disordered environments. Sparse non-Hermitian random matrices arise…
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…
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…
All dynamical systems of biological interest--be they food webs, regulation of genes, or contacts between healthy and infectious individuals--have complex network structure. Wigner's semicircular law and Girko's circular law describe the…
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…
We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different value of correlation among their entries. Spectra of…
Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however,…
We propose a theoretical framework to study the eigenvalue spectra of the controllability Gramian of systems with random state matrices, such as networked systems with a random graph structure. Using random matrix theory, we provide…
The principal eigenvalue $\lambda$ of a network's adjacency matrix often determines dynamics on the network (e.g., in synchronization and spreading processes) and some of its structural properties (e.g., robustness against failure or…
Eigenvalues statistics of various many-body systems have been widely studied using the nearest neighbor spacing distribution under the random matrix theory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplex…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…
Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network,…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define…
The spectral graph theory provides an algebraical approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the…