ExpressionsByAtom and ExpressionsAtomsHypergraph property

[maxitg]

The problem

"ExpressionsByAtom" property will return an association <|atom1 -> {expression1, ...}, atom2 -> {expression2, ...}|> showing which atoms appear in which expressions.

It should take the same arguments as "Expressions" property, i.e., to retrieve the result for the last state only, throughout the entire history, for a particular foliation, etc.

"ExpressionsAtomsHypergraph" will just return the values of the association above. It is a hypergraph with expressions at vertices, and hyperedges indicating which of those expressions are adjacent. It is a complement of the "AtomsExpressionsHypergraph" (also known as the spatial graph).

Possible solution

Here is the code that does that for the final state.

ExpressionsAtomsHypergraph[wmo_] := 
 Module[{ix = wmo["StateEdgeIndicesAfterEvent", -1], es}, 
  Values[Merge[
    Association @@@ (Thread /@ 
       Thread[wmo["AllExpressions"][[ix]] -> ix]), Identity]]]

In[] := ExpressionsAtomsHypergraph[
 WolframModel[{{{x, y}, {x, z}} -> {{x, z}, {x, w}, {y, w}, {z, 
      w}}}, {{0, 0}, {0, 0}}, 2]]
Out[] = {{7, 8, 9, 11, 12}, {7, 10, 11, 13, 14}, {8, 9, 10}, {12, 13, 14}}