The circumference of a graph is the length of any longest cycle in a graph. Hamiltonian graphs on n>1 vertices therefore have circumference of n. For a cyclic graph, the maximum element a_(i j) of the detour matrix over all adjacent vertices (i, j) is one smaller than the circumference. The graph circumference of a self-complementary graph is either n (i.e., the graph is Hamiltonian), n - 1, or n - 2. Circumferences of graphs for various classes of nonhamiltonian graphs are summarized in the table below.

almost Hamiltonian graph | detour matrix | girth | graph cycle | graph diameter | graph eccentricity | graph radius | Hamiltonian number | longest path