Recursive CTEs can also be used quite well for that: Waiting for PostgreSQL 14 – SEARCH and CYCLE clauses – select * from depesz;

I was also going to recommend the book-exploring-graphs-with-elixir

There’s also Apache AGE which people using Postgres might be opting for:

Apache AGE is a PostgreSQL extension that provides graph database functionality. The goal of Apache AGE is to enable users of Postgres to use graph query modeling in unison with Postgres’ existing relational model.

Postgres seems to have it all these days, graph extensions, NoSQL, Hstore, etc

It is not common the usage with elixir, but it is not inexistente, there are drivers for neo4j. For the mix of postgres and neo4j, what would be the reason? If you need multi model database you can check out arangodb, which also have a driver and also have an HTTP API, same as neo4j

Exploring Graphs with Elixir (PragProg) deals with graph databases using elixir. In particular, Bolt Sips is utilised to access Neo4J. Using Bolt Sips, one may employ Cypher to query Neo4J.

If your graph needs are treelike/hierarchical this is a great feature PostgreSQL: Documentation: 14: F.21. ltree