Figure 2.

(a) Average neighbours degree $⟨k_{\mathrm{nn}}\left(k\right)⟩$ (green line) for the Hep-Th network and the ensemble ME1 (pink line). (b) For the Hep-Th the ensembles obtained by the ME2 (green line) and ME3 (dark blue line) methods produce uncorrelated networks. (c) Average neighbours degree (green line) for the AS-Internet network and the ensemble obtained using the ME1 (pink line) method showing that ME1 approximates well $⟨k_{\mathrm{nn}}\left(k\right)⟩$. (d) For the AS-Internet the ME2 (green line) and ME3 (dark blue line) produce ensembles that show correlations for the links that include nodes of high degree. The orange dotted line marks the value of the cut-off degree $k_{\mathrm{cut}}=\sqrt{N⟨k⟩}$. The grey dotted vertical line shows the structural cut–off degree obtained from Eq. (6). The dashed horizontal line shows the value ⟨k_nn(k)⟩ = ⟨k²⟩/⟨k⟩ for the uncorrelated network.