Figure 4

All-pairs VCP element population for$\left\{\right|V|,|\mathcal{R}|,P(e_{i,j}),P(r_x\in \mathcal{R}\left)\right\}$. Note the logarithmic heatmap scale on the bottom two $\left|\mathcal{R}\right|=10$ plots, which is necessary to prevent the plots from appearing solid black due to extreme element sparsity. (a)$\left|V\right|=100,\left|\mathcal{R}\right|=3$, (b) |V|=250, $\left|\mathcal{R}\right|=3$, (c)$\left|V\right|=100,\left|\mathcal{R}\right|=10$, (d)$\left|V\right|=250,\left|\mathcal{R}\right|=10$.