[mnd999]

This can be modelled as a regular graph simply by representing the hyper edge as another node with a set of edges. If those are labelled appropriately to differentiate them from regular nodes, it’s straightforward enough to represent it as a regular graph.

[nine_k]

Many things can be represented as more complex structures of simpler things.

It's interesting whether a new formalism allows to express things better, unearth interesting structures not apparent using a more busy formalism, etc.

Compare the Maxwell equations in the wordy original form, and in a highly compact Clifford algebra form.

[galaxyLogic]

Right but doesn't that mean that in essence you will have two types of nodes in your conceptual model. It is no longer that you have just 'nodes' and 'vertices', you will need to have two different types of nodes, and one type of vertex. The new type of node could be called 'hyper-node' perhaps. Else you lose information.