I found that idea so intriguing I made an account.

Have you considered that such a causal graph can be rearranged while preserving the arrows? I'm inclined to say, for example, that by moving your node E to be on the same level - simultaneous with - B and C, and squishing D into the middle, you've done something akin to taking a Lorentz transform?

I would go further to say that the act of choosing a "cut" of a discrete causal graph - and we assume that B, C, and D share some common ancestor to prevent completely arranging things - corresponds to the act of the choosing a reference frame in Minkowski space. Which makes me wonder if max-flow algorithms have a continuous generalization.

edit: in fact, max-flows might be related to Lagrangians. See this.