# Quantity of Hamiltonian cycles

If I have four vertices, each of which are adjacent to two others, how are the Hamiltonian circuits for those vertices typically counted? If I envision the unit circle of the real plane’s axis intersection points as the vertices in question, the unit circle indicates at least one path; is it ever convention in such a case to indicate more than one path, i.e. depending on starting point, direction, etc.?

• It is conventional to count just one Hamiltonian cycle independent of its starting point. – David G. Stork Apr 20 at 20:44