I understand that you are looking for labeled link relationships. As such I think Neo4j is the only DB, which helps you.
A long time ago, I tried ArangoDB which has some promising graph features. But I didn't get used to AQL language.
Maybe can find more here: nosql-database.org
Edit: For bidirectional relationships where the relation itself must not have properties, I use RethinkDB. If the relationship must have properties, I put them into a document and join them like any other table, supported by a secondary index. Embedded arrays work only for a small set of data, as I feel.