Fig 6. Comparison of hierarchies for twitter-like RSBMs.

The parameters are p = q = 0.5, R = 32, s varies in [0, s_max], with s_max = 0.448. Each point refers to a single realisation of the ensemble. The circles represent the pairs $(h_1^{*},h_1^{\left(p\right)})$, i.e. the optimal hierarchy $h_1^{*}$ computed with agony and the one of the planted hierarchy $h_1^{\left(p\right)}$. The stars represent $(h_1^{*},{\overline{h}}_1^{*})$ where ${\overline{h}}_1^{*}$ is the theoretical hierarchy of Eq (8) with the parameters of the SBM estimated via GraphTool. Finally, s_m is the theoretical resolution threshold and $s_{{\overline{h}}^{\left(p\right)}=0}$ is the theoretical value of s for which the estimate for the planted hierarchy is zero.