Maybe I'm just not skilled enough to handle such a workload with Postgres. But Neo4j handled it easily
Graph databases have a very narrow usecase, and it's almost always in relation to people - at least ime.
Though the data type isn't really important for the performance question, the amount of data selected is. So a 6-level depth graph of connections that only connect 2-3 entities would never get into performance issues. You'd be able to go way beyond that too with such a narrow window. (3 entity Connections on 6 level join would come out to I believe ~750 rows)
If you're modeling something like movies instead, with >10 actors per production you're looking at millions of rows.
https://github.com/joelonsql/graph-query-benchmarks
I haven't tried the latest versions of both databases though.