Figure 4
Rich percolation transition behaviors in the star-like interdependent system of four random network layers with an identical degree distribution. For different values of the tolerance parameter α, (a) the sizes of the giant components, SA, SC, SD versus the Poisson degree distribution parameter z, and (b) the size of the giant component SB versus z, where the dotted vertical lines mark the percolation threshold for B. The solid curves are theoretical predictions while the symbols are direct simulation results. The network size is N = 105. Each data point is the result of averaging over 20 independent statistical realizations. The remarkable phenomenon of mixed percolation transitions occurs for intermediate α values (e.g., α = 0.8 and α = 0.7), where the hub network layer exhibits a discontinuous transition but each peripheral network layer exhibits double transitions: one continuous and another discontinuous.
