On the estimation of percolation thresholds for real networks

The percolation threshold is the critical point at which a giant connected component emerges for the first time in the percolation process. Its theoretical estimation has recently gathered much attention, especially for real networks with complicated structures. However, the theoretical methods so far mainly provide lower bounds of the percolation threshold with non-negligible errors. In this paper, we first generalize the existing message passing algorithm by considering the independence of variables in iteration equations. We then give the exact implicit expressions of the site and bond percolation thresholds based on the correction δ_s(b). The experimental results show that the correction is strongly related to network structural properties so that we can predict it by the gradient boosting regression model. Finally, we take the predicted correction δ_s(b) to our theoretical framework and show that our estimates of site and bond percolation thresholds on 209 real networks are more accurate than those of the state-of-the-art methods.