Percolation threshold

Summary

The percolation threshold of a graph, also called its critical probability, is a value $p_c$ of the parameter $p$ of percolation. At $p_c$ an infinite open cluster starts to appear. Below $p_c$ all open clusters are finite almost surely, and above $p_c$ there is an infinite open cluster almost surely. It depends on the graph and on the choice of bond or site percolation. Exact values are known only for a few graphs, such as $p_c = 1/2$ for bond percolation on the square lattice.