Hypergraphs generalize graphs by allowing edges that connect multiple nodes simultaneously. They are powerful tools for modeling higher-order relationships in data and are increasingly important in geometric and topological deep learning.Expertise level: ⭐⭐⭐
I wrote the implementation of the conversion to simplicial complex to illustrate the combinatorial nature of the generation of simplices from the hyperedges. I select a very simple, minimalist hypergraph and showed that it generate very large Laplacian matrices (displayed as dense array for sake of clarity).
Alternatively the hypergraph can be converted into a cell or even a combinatorial complex (I have not evaluated) although I am not sure whether it reduces complexity.
I wrote the implementation of the conversion to simplicial complex to illustrate the combinatorial nature of the generation of simplices from the hyperedges. I select a very simple, minimalist hypergraph and showed that it generate very large Laplacian matrices (displayed as dense array for sake of clarity).
Alternatively the hypergraph can be converted into a cell or even a combinatorial complex (I have not evaluated) although I am not sure whether it reduces complexity.