Fig. 3. The process of network percolation under maximum flow rule in the real-world FW network.

Diverse networks demonstrate distinct phase transition points, with a delayed percolation transition indicating a diminished resilience of the network at that juncture. Near the critical percolation threshold $q_{\mathrm{c}}$, the size of the giant component G drops sharply, and the size of the second giant component SG reaches its peak. a–d FW networks formed by human activities in various fields. e, f FW networks formed by species predation relationships in nature.