How do I guarantee that a DAG stays acyclic after insertion of a node?

You could also store reverse links and just check that the terminus node of the edge being added does not appear in any of the parent nodes of the origin node. This would be faster than doing a full cycle detection. Essentially this would be a shortest path algorithm on the reverse links, which for a DAG ought to be a linear operation.

If all of the new edges are from the new vertex you won't ever create cycles.

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