FIG. 2.

Analysis of effectiveness and robustness of numerical methods on RRN. (a) Numerical distribution of outbreak sizes in SIR model for $\lambda =0.10$ (circles), $\lambda =1/9$ (triangles), and $\lambda =0.12$ (squares), where blue solid, red short dash, and black dot lines represent the theoretical distributions given by Eq. (A4). (b) χ vs. λ, where only the small outbreak sizes with $\rho \le r_c$ are considered to numerically count χ. (c) Δ vs. λ, where the lump is assumed to be located at r_c in the theoretical distribution diagram when $\lambda >{\lambda }_c$. In (b) and (c), “triangles,” “circles,” and “diamonds” denote cutoff values r_c = 0.05, 0.2 and 0.4, respectively. The parameters are chosen as $N={10}^4$ and k = 10. The results are averaged over ${10}^2\times {10}^6$ independent realizations on 10² networks.