A Semi-Analytic Algorithm to Estimate Clusters With Loops in Percolation on Real Networks

Estimating the percolating cluster fraction is central to many percolation models. For real networks, the total size of clusters with loops can be considered a plausible metric for this fraction. In this paper, we develop a semi-analytic algorithm to estimate clusters with loops for both site and bond percolation via modifying the message passing algorithm. We compared the estimates of the original message passing algorithm and our modified version with simulation results on four real networks. Our findings suggest that our modified algorithm can achieve accuracy for any real network, provided that a sufficient number of possible states following site or bond occupation are selected and analyzed to calculate the final estimate.