Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as a result, denoted C(p) is known as the reliability polynomial of G. The reliability polynomial is directly expressible in terms of the Tutte polynomial of a given graph as C(p) = (1 - p)^(n - c) p^(m - n + c) T(1, p^(-1)), where n is the vertex count, m the edge count, and c the number of connected components (Godsil and Royle 2001, p. 358; error corrected).

rank polynomial | Tutte polynomial