A graph is Eulerian if it has a path in the graph that visits each vertex exactly once. A digraph is Eulerian if it has a directed path in the graph that visits each vertex exactly once. Such a path is called an Eulerian circut. Unconnected graphs can be Eulerian, but all vertices of degree greater than 0 of a graph (or all vertices of degree greater than 0 in the underlying graph of a digraph) must belong to a single connected component.