 Percolation cluster

In bond percolation, a percolation cluster is a connected component of a graph formed by the open edges, with every graph vertex retained. In site percolation, it is a connected component of a graph of the subgraph induced by the open graph vertices. Write $C(x)$ for the cluster containing $x$; for site percolation set $C(x)=\varnothing$ when $x$ is closed.