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I'm looking at a specific class of DAGs, namely those DAGs such that any path from $u$ to $v$ has the same length. Informally, we don't allow "skip-level" edges. I understand these graphs are the DAGs that are their own transitive reduction.

I added a small number of examples below.

Thank you!

A few example graphs

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    $\begingroup$ I have seen these called "layered digraphs" but I don't know how common that is. $\endgroup$ Commented Dec 4, 2020 at 12:30
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    $\begingroup$ (+1) "Layered" is definitely the commonly-used term here. $\endgroup$ Commented Dec 4, 2020 at 18:30

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