The rank polynomial R(x, y) of a general graph G is the function defined by R(x, y) = sum_(S⊆E(G)) x^(r(S)) y^(s(S)), where the sum is taken over all subgraphs (i.e., edge sets) and the rank r(S) and co-rank s(S) of the subgraph S is given by r(S) | = | n - c s(S) | = | m - n + c for a subgraph with n vertices, m edges, and c connected components.

chromatic polynomial | flow polynomial | rank matrix | reliability polynomial | Tutte polynomial