Does generalizing to hypergraphs ease this in any way? The cost-benefit trade-off seems to be greater computational complexity for potentially unobserved insights.
- they provide a type for conclusions that span several nodes, eg a ring’s interior is a node that represents the existence of a ring (and so cache your analysis conclusions)
- they allow for generalization by placing nodes within a cell, eg “people who make $50k-$150k/yr” can be a collection of people within a cell (and we can talk about aggregated edges from that cell’s interior to other objects)
A third (but useful in a different context):
- logic can be represented as hypergraphs and deduction rules on them
See for instance, the ngraph coarsen procedure that reduces communities and their interrelations to single nodes connected to other community nodes [0].
But my intuition is that caching derived graphs and caching computed cells will be similar — and might even be two conceptual frameworks on equivalent data.
> Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph
Where the relation is one-to-one, so there is a Levi graph for every hypergraph and the reverse is also true.