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How would you calculate something like a Hausdorff dimension of a graph given there’s no unique embedding in Euclidean space, but we still think of (for eg) bushy vs sparse branching etc? A long skinny DAG with few branches should be lower dim than dense random graph for eg 🤔
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Maybe average or median fan-out per node for a directed graph? Or average number of choices (also fan-out) at each node for a DAG? Which flavor or quality are trying to capture, transferred over from the original scalar?
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If you squint at a (biological) tree or cauliflower it looks like a sankey diagram of an aggregate flow. The coarse topology of that flow given a resolution level. Like a recursive approximation of min-cut-max-flow view. DAGs are the easiest case.
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