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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…
One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…
Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently…
Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…
We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
In a recent paper, it has been suggested that the controllability of a diffusively coupled complex network, subject to localized feedback loops at some of its vertices, can be assessed by means of a Master Stability Function approach, where…
Many real networks have been found to have a rich degree of symmetry, which is a very important structural property of complex network, yet has been rarely studied so far. And where does symmetry comes from has not been explained. To…
Neurons in the primary visual cortex are more or less selective for the orientation of a light bar used for stimulation. A broad distribution of individual grades of orientation selectivity has in fact been reported in all species. A…
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…
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…
We propose a real-space approach explaining and controlling the occurrence of edge-localized gap states between the spectral quasibands of binary tight binding chains with deterministic aperiodic long-range order. The framework is applied…
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several…
Spectra of real world networks exhibit properties which are different from the random networks. One such property is the existence of a very high degeneracy at zero eigenvalues. In this work, we provide possible reasons behind occurrence of…
We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
A nearest-neighbor tight-binding model on a tree structure is investigated. The full energy spectrum of the normalized Hamiltonian can be expressed in terms of successively increasing number of contributions at any finite step of…
We comprehensively studied the morphology of the self-organized effective network structures that form in simple coupled maps with interelement synchronization-dependent connection changes. Based on the parameter values, the spontaneous…
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…
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…