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. 2015 Dec 17;6:10179. doi: 10.1038/ncomms10179

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(a–c) Localization of the leading eigenvectors for null model 1 versus empirical mutualistic networks (where , with q₁=v₁, u₁ or w_H, with right eigenvector v₁ in red, left eigenvector u₁ in blue and reactive eigenvector w_H in green). Points represent average value of 1,000 randomizations, bars indicate the standard deviation. 1:1 line represents the value of the empirical mutualistic networks. (d–f) Same for null model 2. (g) Number of (localized) components as a function of the community size: a significant correlation is observed (Spearman Rank Test=0.715). (h) Effect of the localization on the asymptotic amplitude for the simulated perturbation ξ_all on empirical mutualistic networks with respect to null model 1 . In ≈85% of the cases, the perturbation amplitude is significantly attenuated (P value≤0.05). (i) P values of the observed values of localization and asymptotic amplitudes in empirical networks with respect to null model 1. Parameters here are δ=0.5 and γ₀=1.

Inline graphic — (a–c) Localization of the leading eigenvectors for null model 1 versus empirical mutualistic networks (where , with q₁=v₁, u₁ or w_H, with right eigenvector v₁ in red, left eigenvector u₁ in blue and reactive eigenvector w_H in green). Points represent average value of 1,000 randomizations, bars indicate the standard deviation. 1:1 line represents the value of the empirical mutualistic networks. (d–f) Same for null model 2. (g) Number of (localized) components as a function of the community size: a significant correlation is observed (Spearman Rank Test=0.715). (h) Effect of the localization on the asymptotic amplitude for the simulated perturbation ξ_all on empirical mutualistic networks with respect to null model 1 . In ≈85% of the cases, the perturbation amplitude is significantly attenuated (P value≤0.05). (i) P values of the observed values of localization and asymptotic amplitudes in empirical networks with respect to null model 1. Parameters here are δ=0.5 and γ₀=1.