How should I call a graph that is not a multigraph?

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Vocabulary question : A multigraph is a graph that can have several identical edges (same vertices, same direction if directed).

Is there an official name for a graph that is not a multigraph ?

  • "Graph" seems too generic, as this describes any kind of graph
  • "Simple graph" is already an undirected "not multi" graph with no loops

I didn't manage to find better names for a graph which only constraint would be "no identical edges"... "Monograph" ?