Table 3. Comparison of the theoretical predictions and experimental data results.

Binned degree	Theory	Exp. data
1	0.010	0.012
2	0.020	0.024
4	0.040	0.013
8	0.079	0.029
16	0.152	0.089
32	0.281	0.174
64	0.483	0.256
128	0.732	0.513
256	0.928	0.570
512	0.994	0.511
1024	0.999	0.333

The theoretical analysis derives a simple mathematical expression (Eq. 2 in SI) that can estimate the fraction of critical nodes in bipartite networks.