Fig. 10

Linear models of the robustness R as a function of the modularity indicator Q (R = α·Q + β) and the average node degree \(\left\langle k \right\rangle\) (R = α ·\(\left\langle k \right\rangle\) + β). Top row: model networks (red points); Bottom row: real-world social networks (blue points). A, C Model networks are generated with N = 10,000, \(\left\langle k \right\rangle\) = 4, m = 5 and with increasing modularity by varying the parameter w. B, D Model networks are generated with N = 10,000, m = 5, w = 0.9 and varying \(\left\langle k \right\rangle\) in the interval (4, 32). Statistical outcomes of the linear model parameters (slope α and intercept β): A R_IB versus Q: α = − 0.2, β = 0.35, p-value = 0.01; B R_IB versus \(\left\langle k \right\rangle\): α = 0.01, β = 0.14, p-value < 0.001; C R_ID versus Q: α = − 0.15, β = 0.31, p-value < 0.001; D R_ID versus \(\left\langle k \right\rangle\): α = 0.01, β = 0.1, p-value < 0.001; E R_IB versus Q: α = − 0.26, β = 0.37, p-value = 0.001; F R_IB versus \(\left\langle k \right\rangle\): α = 0.004, β = 0.18, p-value = 0.16; G R_ID versus Q: α = − 0.22, β = 0.36, p-value = 0.035; H R_ID versus \(\left\langle k \right\rangle\): α = 0.003, β = 0.2, p-value = 0.2