A relatively simple model for percolation properties of real networks

- We develop a relatively simple model to study percolation properties of real networks.
- We derive the exact expression of the threshold for both site and bond percolation.
- We compare estimates of our model and the message passing algorithm as well as simulation results on real networks.
- We give explanations on the discrepancies between the estimates and the simulation values.

Analyzing percolation rules of real networks has some great realistic significance. In this paper, we develop a relatively simple model based on generating function method to study percolation properties of real networks. We construct our model for both site and bond percolation, compare its estimates with those of the message passing algorithm and simulation results on computer-generated networks as well as practical networks, and discuss causes of the inaccuracy. The conclusions show that the accuracy of our model could be accepted though it is lower than that of the message passing algorithm and the discrepancies between the estimates of our model and the simulation values mainly come from the disagreement of those real networks with the model hypotheses.