Adding Hypergraph object

[daneelsan]

Changes

• Trying to solve #494.
• Adding a basic Hypergraph object, accessors and upvalues.

Comments

• Various designs questions:

  • ~How to represent the Hypergraph object in a notebook? Interpretation boxes (e.g. SparseArrays) or Graph-like plots?~ Decided on using a summary box.
  • ~The symbol Hyperedge is private for now. Should this be exposed?~ Decided to not use the symbol yet, just a list.
  • ~Should we consider hypergraphs with mixed types of Hyperedges? See https://github.com/maxitg/SetReplace/issues/494#issuecomment-720580460~ Decided to use "global" symmetries for now.

• "ordered" was added (needs to be discussed) because many functions in WFR made the distinction. See:

  • https://resources.wolframcloud.com/FunctionRepository/resources/IsomorphicOrderedHypergraphQ/
  • https://resources.wolframcloud.com/FunctionRepository/resources/FindOrderedHypergraphIsomorphism/

ToDo

• [ ] Fix HypergraphPlot
• [ ] Plot the hypergraph if it is not big (in the summary box)
• [ ] Tests
• [ ] Documentation
• [ ] More upvalues and/or redesign other functions to return Hypergraph (e.g. RandomHypergraph)

Examples

• Create a random Hypergraph ("Ordered" by default):

(*In[]:=*) {8, 4} // RandomHypergraph // Hypergraph

• Create a "Cyclic" Hypergraph:

(*In[]:=*) Hypergraph[{{1, 1, 1}}, True]

• Some accessors:

hg = Hypergraph[{{}, {}, {1, 2, 3}}];

In[]:= EdgeList[hg]
Out[]= {{}, {}, {1, 2, 3}}

In[]:= VertexList[hg]
Out[]= {1, 2, 3}

In[]:= HypergraphSymmetry[hg]
Out[]= "Ordered"

• Information:

(*In[]:= *) Information[Hypergraph]

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