Fig 1.
Integration of fragmented transportation networks with similar structures to evaluate the synergistic effect.
(A) Schematic of the experimental procedure. (B) Example of the integration of two fragmented networks generated from a grid network.
Fig 2.
Synergistic effect in different network types: (A) Maximum flow as a function of the link survival ratio r and dissimilarity d. (B) Size of the giant component. We evaluated 0 ≤ r ≤ 0.05 for the social network because it had a much greater link density than the other networks. (C) Propensity of each node to be included in the giant component under controlled conditions. The error bars in the graphs represent the standard deviation computed based on 1000 samples.
Fig 3.
Synergistic effect in integrated networks according to the degree of the core–periphery structure (γ): (A) Maximum flow, (B) size of giant component, and (C) distribution of the propensity of each node to be included in the giant component. We set δ = 0 (see Fig A3 in S1 Appendix for the results for δ = 1). Network statistics for fragmented networks (δ = 0, γ = 10): (D) probability of the source and sink nodes being included in the giant component and (E) maximum flow depending on whether the source and sink nodes are core and/or peripheral nodes. The error bars represent the standard deviation computed based on 1000 samples.
Fig 4.
Magnitude of the synergistic effect of network integration vs the cost of increasing the giant component for different network structures with different numbers of nodes (N) and links (L).
Fig 5.
Synergistic effect of integrating networks with different structures.
Two fragmented networks were integrated with the same link survival ratio r except for the social network. In this case, r/10 was used given its particularly high link density. The shaded area shows the separate maximum flow for each fragmented network. The error bars represent the standard deviation computed based on 1000 samples.
Fig 6.
Synergistic effect of integrating networks with different core–periphery structures.
(A) Types of integrated networks. CP1 and CP2 were core–periphery networks with different core nodes (δ = 0, γ = 10). The random network was generated by setting δ = 0 and γ = 0. (B) Maximum flow in the integrated networks. (C) Giant component size in the integrated networks. (D) Distribution of the propensity of each node to be in the giant component. The error bars represent the standard deviation computed based on 1000 samples.