Perculation theory has found broad application to porous media in the context of oil and gas exploitation. But it also helps to calculate the stability of networks like the WWW.
Percolation deals with the effects of varying the richness of interconnections present in a random system. So percolation theory was developed to mathematically deal with disordered media, in which the disorder is defined by a random variation in the degree of connectivity. Percolation theory tells us that if we randomly remove nodes, then at some critical fraction, the network should fragment into tiny, non-communicating islands of nodes.