Related papers: Spectral Analysis and the Dynamic Response of Comp…
Users of social networks display diversified behavior and online habits. For instance, a user's tendency to reply to a post can depend on the user and the person posting. For convenience, we group users into aggregated behavioral patterns,…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
The adjacency and Laplacian matrices of complex networks with two species of nodes are studied and the spectral density is evaluated by using the replica method in statistical physics. The network nodes are classified into two species (A…
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…
We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
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 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…
The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$.…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…
The spectral properties of the adjacency (connectivity) and distance matrix for various types of networks: exponential, scale-free (Albert--Barabasi) and classical random ones (Erdos--Renyi) are evaluated. The graph spectra for dense graph…
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,…
Covariance matrix of heights measured relative to the average height of a growing self-affine surface in the steady state are investigated in the framework of random matrix theory. We show that the spectral density of the covariance matrix…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
Using methods from random matrix theory researchers have recently calculated the full spectra of random networks with arbitrary degrees and with community structure. Both reveal interesting spectral features, including deviations from the…