An Eulerian Trail which starts and ends at the same Vertex. In other words, it is a Cycle which uses each Edge exactly once. The term Eulerian Cycle is also used synonymously with Eulerian circuit. For technical reasons, Eulerian circuits are easier to study mathematically than are Hamiltonian Circuits. As a generalization of the Königsberg Bridge Problem, Euler showed (without proof) that a Connected Graph has an Eulerian circuit Iff it has no Vertices of Odd Degree.
See also Euler Graph, Hamiltonian Circuit