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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