Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks
نویسندگان
چکیده
Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term correlation. We study the spectral fluctuations of the adjacency of networks using random-matrix theory. We consider the influence of the spectral unfolding, which is a necessary procedure to remove the secular properties of the spectrum, on different spectral statistics. We find that, while the spacing distribution of the eigenvalues shows little sensitivity to the unfolding method used, the spectral rigidity has greater sensitivity to unfolding.
منابع مشابه
Cospectral graphs for both the adjacency and normalized Laplacian matrices
In this note we show how to construct two distinct bipartite graphs which are cospectral for both the adjacency and normalized Laplacian matrices by “unfolding” a base bipartite graph in two different ways.
متن کاملThe machine learning process in applying spatial relations of residential plans based on samples and adjacency matrix
The current world is moving towards the development of hardware or software presence of artificial intelligence in all fields of human work, and architecture is no exception. Now this research seeks to present a theoretical and practical model of intuitive design intelligence that shows the problem of learning layout and spatial relationships to artificial intelligence algorithms; Therefore, th...
متن کاملUniversality in complex networks: random matrix analysis.
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world, and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory. Second, we show an analogy between the onset of small-world behavior, quantified by the s...
متن کاملSpectral Density of Complex Networks with a Finite Mean Degree
In order to clarify the statistical features of complex networks, the spectral density of adjacency matrices has often been investigated. Adopting a static model introduced by Goh, Kahng and Kim, we analyse the spectral density of complex scale free networks. For that purpose, we utilize the replica method and effective medium approximation (EMA) in statistical mechanics. As a result, we identi...
متن کاملCartesian decomposition of matrices and some norm inequalities
Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012