Concentration of Small world-Networks and application of spectral algorithms

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Laala Zeyneb, Belguerna abderrahmane

Abstract

Recent researches on statistical network analysis has strongly included the random matrix theory. The principal goal of random matrix theory is to provide a knowledge of many properties of matrices such as the statistics of matrix eigenvalues with elements taken randomly from various probability distributions. In this paper, we present some results on the concentration of the adjacency and laplacian matrices around the expectation under the small-world network. We also present some relevant network model that may be of interest to probabilists looking for new directions in random matrix theory as well as random matrix theory tools that may be of interest to statistician looking to verify the features of network algorithm. Application of some results to the community detection problem are discussed

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