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10.1038/s41598-017-01010-0 http://scihub22266oqcxt.onion/10.1038/s41598-017-01010-0 C5430689!5430689!28442760     free     free     free Deprecated: Implicit conversion from float 217.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534       Sci+Rep 2017 ; 7 (ä): ä Nephropedia Template TP {{tp|p=28442760|t=2017. Localization of Laplacian eigenvectors on random networks |pdf=|usr=}}{{28442760}} gab.com Text Localization of Laplacian eigenvectors on random networks JO: Sci Rep http://www.kidney.de/pget.php?&tw=1&pmid=28442760 #FOAvip In large random networks, each eigenvector of the Laplacian matrix tends to localize on a subset of network nodes having similar numbers of edges, namely, the components of each Laplacian eigenvector take relatively large values only on a particular subset of nodes whose degrees are close. Although this localization property has significant consequences for dynamical processes on random networks, a clear theoretical explanation has not yet been established. Here we analyze the origin of localization of Laplacian eigenvectors on random networks by using a perturbation theory. We clarify how heterogeneity in the node degrees leads to the eigenvector localization and that there exists a clear degree-eigenvalue correspondence, that is, the characteristic degrees of the localized nodes essentially determine the eigenvalues. We show that this theory can account for the localization properties of Laplacian eigenvectors on several classes of random networks, and argue that this localization should occur generally in networks with degree heterogeneity. Twit Text FOAVip Localization of Laplacian eigenvectors on random networks ????Sci Rep http://www.kidney.de/pget.php?&tw=1&pmid=28442760 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=28442760 #FOAvip English Wikipedia <ref>{{Cite pmid|28442760}}</ref> Localization of Laplacian eigenvectors on random networks #MMPMID28442760 Hata S; Nakao H Sci Rep 2017[]; 7 (ä): ä PMID28442760show ga In large random networks, each eigenvector of the Laplacian matrix tends to localize on a subset of network nodes having similar numbers of edges, namely, the components of each Laplacian eigenvector take relatively large values only on a particular subset of nodes whose degrees are close. Although this localization property has significant consequences for dynamical processes on random networks, a clear theoretical explanation has not yet been established. Here we analyze the origin of localization of Laplacian eigenvectors on random networks by using a perturbation theory. We clarify how heterogeneity in the node degrees leads to the eigenvector localization and that there exists a clear degree-eigenvalue correspondence, that is, the characteristic degrees of the localized nodes essentially determine the eigenvalues. We show that this theory can account for the localization properties of Laplacian eigenvectors on several classes of random networks, and argue that this localization should occur generally in networks with degree heterogeneity. äLocalization of Laplacian eigenvectors on random networks (epmc).pdf DeepDyve Pubget Overpricing