This comment (I think) makes your point clearer to me. The problem isn’t so much in the “send your directed graph to a metric space” as it is “choose a basis of your metric space.”
I think there is a sense in which you could find “less arbitrary” choices, but I don’t think an algorithm exists among humans to find one reliably so I think you’re right.
This comment (I think) makes your point clearer to me. The problem isn’t so much in the “send your directed graph to a metric space” as it is “choose a basis of your metric space.”
I think there is a sense in which you could find “less arbitrary” choices, but I don’t think an algorithm exists among humans to find one reliably so I think you’re right.