I'm pretty sure I saw some subgraph isomorphism libraries the last time I was working with Neo4j, so definitely by now they exist and are well-developed.

But if subgraph isomorphism search is infeasible time-wise I have to rethink how I'm going to code things.

I'm wanting to store almost every known commutative diagram in popular categories (from category theory or math) in a gigantic database.

For example, if it takes 40 seconds to search a million graph database where the graphs are disconnected (as far as the parts go that you're trying to do an isomorphic subgraph on), and there are < 20 nodes per graph on average, then I would want to maybe split up the database into one database per category.