# Necessary and sufficient condition for a directed graph be Eulerian circuit and Hamilton cycle

I have knowledge of the necessary and sufficient condition for an undirected graph contains a Hamiltonian cycle and an Eulerian circuit, but is there a necessary and sufficient condition for directed graphs?

common sense tells me that the degree of input minus output degree of each vertex must be zero, but do not know if I'm right (this is for the euler circuit)

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The graph has a finite set of vertices – franvergara66 Nov 13 '11 at 5:18

If you can find Hamiltonian cycles in an undirected graph, you can find them in directed graphs too by replacing each vertex by a linear sequence of three vertices *---*---* and connect all incoming edges to one of the end nodes and all the outgoing edges to the other end node. After that you don't need to remember the direction of the edges.