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0.4.2.3 Euler Cycles

A cycle in a graph is a traversal which visits no node more than once. An Euler cycle is a special cycle that traverses all the edges in a graph and visits every node at least once. It can be proven that an Euler cycle can exist in a graph if and only if all vertices are of even degree. That is to say, the must be an even number of edges emanating from every vertex in the graph.