# Does Dirac's theorem on Hamiltonian cycles only apply to undirected graphs?

Does Dirac's theorem on Hamiltonian cycles only apply for undirected graphs? If the theorem applied to directed graphs, the graph with the following adjacency list should have a Hamiltonian cycle, but I can't find one.

$0$: $1$ $2$ $3$

$1$: $2$ $3$

$2$: $1$ $3$

$3$: $1$ $2$

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Yes Dirac Theorem is for undirected graphs, directed variation is this(is not by dirac): If $G$ is a strongly connected graph and $\delta^+(G)+\delta^-(G) \ge n$. $\delta^+(G)$ is minimum out degree and $\delta^-(G)$ is minimum in degree of $G$. –  Saeed Apr 23 at 20:56

Their requirements, however, were that each vertex should have both out-degree and in-degree of at least $n/2$, which is not the case in your graph.
One of the original conditions of GHOUILA-HOURI, as Saeed mentioned, is that the graph is strongly connected. In fact, the degree conditions are strong enough for only diameter $\leq 2$ graphs to be considered.