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?
-
-
-
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.
- 5 more replies
New conversation -
-
-
I'm pretty sure a graph simply has a hausdorff dimension of zero since the nodes are points and there's only one link between any two points. I suppose you could think of a graph with an uncountable number of nodes by constructing some set but that sounds a bit iffy
-
You're technically correct, but that's why I said something *like* a hausdorff dimension that captures the sense of spatial density of an embedded graph
End of conversation
New conversation -
-
-
can take e.g. the average degree / 2, although i don't know how useful this is. you can think of the average degree / 2 localized in a region of a graph as being a "local dimension" which can then vary across regions of the graph
-
ah no, this doesn't really capture enough structure. better: every graph is a metric space with metric given by the length of the shortest path and then there's a notion of local dimension given by how fast balls wrt this metric grow
- 1 more reply
New conversation -
-
-
Start at a vertex, look at the number of first neighbors, second, ... . Repeat and average for all vertices. Try fitting r^{d-1},where r is the order of the neighbor. This should be *a* valid dimension, though not sure if it matches the Hausdorff dimension.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Some ideas here: https://arxiv.org/pdf/1808.01079.pdf …
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
errrr ????
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.
