Universality
The universality principle states that the value of pc is connected to the local structure of the graph, while the behavior of clusters below, at, and above pc are invariant with respect to the local structure, and therefore, in some sense are more natural quantities to consider. This universality also means that for the same dimension independent of the type of the lattice or type of percolation (e.g., bond or site) the fractal dimension of the clusters at pc is the same.
Read more about this topic: Percolation Theory