How does the running for tiime for subgraph isomorphism search scales with number of disconnected components?

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.

Can you share more details of what exactly you want to do?

If you can provide additional constraints, e.g. labels, rel-types, key properties, etc. that reduces the effort. It should also be well parallelizable. In APOC there is a procedure to compare subgraphs and return the delta but it's not heavily optimized.