HypergraphDistanceMatrix

[daneelsan]

The problem

The function HypergraphDistanceMatrix should compute the distance between any 2 vertices in the hypergraph, similar to GraphDistanceMatrix, where (hypergraph) distance is (roughly) defined as the minimum length of a path that connects both vertices.

Possible solution

One "easy" solution is to use both HypergraphToGraph and GraphDistanceMatrix to compute this:

HypergraphDistanceMatrix[hg_, "Directed"] :=
  GraphDistanceMatrix[HypergraphToGraph[hg, "DirectedDistancePreserving"]]

HypergraphDistanceMatrix[hg_, "Undirected"] :=
  GraphDistanceMatrix[HypergraphToGraph[hg, "UndirectedDistancePreserving"]]

In[]:= vertexList = Sort@*Union@*Catenate;

With[{hg = {{x, x, y, z}, {z, w}, {w, a}}},
 Table[
   {method, TableForm[HypergraphDistanceMatrix[hg, method], TableHeadings -> Table[vertexList@hg, 2]]},
   {method, {"Undirected", "Directed"}}] // Grid[#, Frame -> All, FrameStyle -> LightGray] &
 ]

Alternative solutions

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Additional context

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