  The critical group K(G) of a directed graph G=(V,E) is the cokernel of the
transpose of the Laplacian matrix of G acting on the integer lattice Z^V. For
undirected graphs G, this has been considered by Bacher, de la Harpe, and
Nagnibeda, and by Biggs. We prove several things, among which are: K(G/p) is a
subgroup of K(G) when p is an equitable partition and G is strongly connected;
for undirected graphs, the torsion subgroup of K(G) depends only on the graphic
matroid of G; and, the `dollar game' of Biggs can be generalized to give a
combinatorial interpretation for the elements of K(G), when G is strongly
connected.
