Two typical analytic models for reverse bond percolation on real networks

Reverse bond percolation is the inverse process of bond percolation, which examines the global connectivity of a network after adding edges with uniform probability. Despite its universal significance, it has not been studied as extensively as bond percolation. This paper investigates two reverse bond percolation scenarios: in the first, any pair of unconnected nodes can be connected, while in the second, only specific pairs can be connected. Two typical bond percolation models, the generating-function-based model and the message passing model, are reconstructed for each scenario to calculate analytical values of the spanning cluster fraction and percolation threshold, respectively. These analytic models are then applied to computer-generated and real-world networks to assess their accuracy. The results reveal that both models have their own strengths. While the message passing model provides more precise values, it requires a significant amount of computational effort and is not ideal for networks with a large number of existing and potential edges. The generating-function-based model is less accurate than the message passing model, but its calculation process is simple, making it suitable for a variety of real-world networks. These two reverse percolation analytic models may complementarily predict percolation properties of real-world networks after the edge-adding process.& COPY; 2023 Elsevier B.V. All rights reserved.