Related papers: Approximating the largest eigenvalue of network ad…
Degree correlation plays a crucial role in studying network structures; however, its varied forms pose challenges to understanding its impact on network dynamics. This study devised a method that uses eigenvalue decomposition to…
Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an…
The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can…
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…
Damage scenarios for large networks are considered. The cascade scenario is described by means of powers of adjacency matrix. More difficult probabilistic variants of the large network damage are modeling by Markov chains. For reliability…
The newly introduced neighborhood matrix extends the power of adjacency and distance matrices to describe the topology of graphs. The adjacency matrix enumerates which pairs of vertices share an edge and it may be summarized by the degree…
For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix, and the distance energy is defined as the sum of the absolute values of the eigenvalues of its distance matrix. We establish lower and…
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…
In this article we investigate normalized adjacency eigenvalues (simply normalized eigenvalues) and normalized adjacency energy of connected threshold graphs. A threshold graph can always be represented as a unique binary string. Certain…
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…
For a connected graph $G$, let $A(G)$ be the adjacency matrix of $G$ and $D(G)$ be the diagonal matrix of the degrees of the vertices in $G$. The $A_{\alpha}$-matrix of $G$ is defined as \begin{align*} A_\alpha (G) = \alpha D(G) +…
We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than…
Let G be a simple connected graph of order n with degree sequence d_1, d_2, ..., d_n in non-increasing order. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer L at most n, we give…
We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green…
The leading eigenpair (the couple of eigenvalue and its eigenvector) or the first nontrivial one has different names in different contexts. It is the maximal one in the matrix theory. The talk starts from our new results on computing the…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
Unsupervised homogeneous network embedding (NE) represents every vertex of networks into a low-dimensional vector and meanwhile preserves the network information. Adjacency matrices retain most of the network information, and directly…
We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…
Generation of realistic topologies plays an important role in determining the accuracy and validity of simulation studies. This study presents a discussion to justify why, and how often randomly generated adjacency matrices may not not…
We investigated the topological properties of stock networks through a comparison of the original stock network with the estimated stock network from the correlation matrix created by the random matrix theory (RMT). We used individual…