Comment by wisnesky

Yes; categories extend traditional graphs with systems of equations. Hypergraphs extend traditional graphs by allowing edges to be between multiple nodes. Most operations on categories are formally undecidable because of the systems of equations; most operations on graphs/hypergraphs are decidable. This makes working with categorical databases a lot like doing computer algebra in e.g. Mathematica and provides a huge increase in expressive power (you can e.g. encode Turing machines with equations.)