相关论文: Approximating the largest eigenvalue of network ad…

We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and…

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…

Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is…

In this paper, we mainly study the trace norm of the adjacency matrix of a graph, also known as the energy of graph. We give the maximum trace norms for the graph and its complement. In fact, the above problem is stated and solved in a more…

In this article, we study Pareto eigenvalues of distance matrix of connected graphs and show that the non zero entries of every distance Pareto eigenvector of a tree forms a strictly convex function on the forest generated by the vertices…

In this Letter we identify the general rules that determine the synchronization properties of interconnected networks. We study analytically, numerically and experimentally how the degree of the nodes through which two networks are…

A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static…

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…

In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…

An eigenvalue of the adjacency matrix of a graph is said to be \emph{main} if the all-1 vector is not orthogonal to the associated eigenspace. In this work, we approach the main eigenvalues of some graphs. The graphs with exactly two main…

In graph signal processing, the graph adjacency matrix or the graph Laplacian commonly define the shift operator. The spectral decomposition of the shift operator plays an important role in that the eigenvalues represent frequencies and the…

The nonbacktracking matrix, and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as non-recurrent epidemics. Here we study the localization of NBC in infinite sparse…

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 study eigenvalue distribution of the adjacency matrix $A^{(N,p, \alpha)}$ of weighted random bipartite graphs $\Gamma= \Gamma_{N,p}$. We assume that the graphs have $N$ vertices, the ratio of parts is $\frac{\alpha}{1-\alpha}$ and the…

Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of…

We study a Gaussian matrix function of the adjacency matrix of artificial and real-world networks. In particular, we study the Gaussian Estrada index---an index characterizing the importance of eigenvalues close to zero. This index accounts…

We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…

We study eigenvalue distribution of the adjacency matrix $A^{(N,p, \alpha)}$ of weighted random bipartite graphs $\Gamma= \Gamma_{N,p}$. We assume that the graphs have $N$ vertices, the ratio of parts is $\frac{\alpha}{1-\alpha}$ and the…

We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and…

Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework…