Hamilton Circuits & Paths Which of the BEST describes a Hamiltonian Path. A path that uses each edge of a graph exactly once and ends at a vertex different from the starting vertex. A path that uses each vertex of a graph exactly once and ends at a vertex different from the starting vertex. A path that uses each edge of a graph exactly once and ends at the starting vertex. A path that uses each vertex of a graph exactly once and ends at the starting vertex.