If you only need a few graph queries then you could just use SQLite, it’s capable of doing it (I have done it before). But writing graph queries in SQL is painful, so I wouldn’t do it if you need more than a handful.
I also really like Neo4J, but the community version is very crippled. Still though, I've worked around it and do hot backups with ZFS and run multiple database processes to support multiple customers.
I don't know of any SQLite-like graph database. I'm still a fan of neo4j.