FIG. 5.

Comparison of theoretical thresholds with numerical thresholds for $\mu <1$. The threshold λ_c vs. k for $\mu =0.1$ (a) and $\mu =0.5$ (b) on RRN. The threshold λ_c vs. γ for $\mu =0.1$ (c) and $\mu =0.5$ (d) on SFN, where solid and empty symbols denote SFN with structural cutoff $k_{\mathit{m}\mathit{a}\mathit{x}}\sim N^{1/2}$ and natural cutoff $k_{\mathit{m}\mathit{a}\mathit{x}}\sim N^{1/\gamma -1}$, respectively. “Circles” and “squares” denote ${\lambda }_c^{\mathit{H}\mathit{M}\mathit{F}}$ and ${\lambda }_p^{\Delta }$, respectively. Inset: λ_c as a function of μ on RRN with $N={10}^4$ and k = 6. The results are averaged over ${10}^2\times {10}^6$ independent realizations on 10² networks.