Chapter 9: Fundamental Physics

Section 12: Evolution of Networks

Identifying subnetworks [in networks]

The problem of finding where in a network a given subnetwork can occur turns out in general to be computationally difficult. For strings the analogous problem is straightforward, since in a string of length n one can ultimately just try each of the n possible starting points for the substring and see for which of them a match occurs. But for a network with n nodes, a similar procedure would require one to check n^k possible configurations in order to find out where a subnetwork of size k occurs. In practice, however, for fixed subnetworks, one can devise fairly efficient procedures. But the general problem of so-called subgraph isomorphism is formally NP-complete.

From Stephen Wolfram: A New Kind of Science [citation]