What are, if they exist, the terminal object in the category of digraphs?

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Is there a terminal object in the category DiGrph? I have looked before online and on here to see if one exists, but I have not had much luck. If there is, what would it look like as a digraph?

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Sure. It's the graph with a single vertex and a single loop at that vertex. If your digraphs don't allow loops, then there is no terminal object, since the graph with one vertex and no edges admits at least two maps to any other nonempty graph (EDIT: and no maps into the empty graph) but is not itself terminal.