Erratum: Localization of Laplacian eigenvectors on random networks

Scientific Reports 7:1121; doi:10.1038/s41598-017-01010-0; Article published online 25 April 2017

This Article contains errors in the Methods section under the sub-heading “Degenerate perturbation theory”, where:

$V_{ij}={}_0|{\alpha }_i⟩L_1{|{\alpha }_j⟩}_0$

should read:

$V_{ij}={}_0⟨{\alpha }_i|L_1{|{\alpha }_j⟩}_0$

In addition,

$W_{kj}={\mathrm{\Sigma }}_{\beta \ne \alpha }({}_0|{\tilde{\alpha }}_k\rangle L_1{|\beta \rangle }_0{}_0\langle \beta |L_1{|{\tilde{\alpha }}_j\rangle }_0)/({{\mathrm{\Lambda }}_0}^{\left(\alpha \right)}-{{\mathrm{\Lambda }}_0}^{(\beta )})$

should read:

$W_{kj}={\mathrm{\Sigma }}_{\beta \ne \alpha }({}_0\langle {\tilde{\alpha }}_k|L_1{|\beta \rangle }_0{}_0\langle \beta |L_1{|{\tilde{\alpha }}_j\rangle }_0)/({{\mathrm{\Lambda }}_0}^{(\alpha )}-{{\mathrm{\Lambda }}_0}^{(\beta )})$