Neo4j replication alternative to Neo4j Enterprise edition?

Update:

This answer has changed. Neo4j is now open core, so the Enterprise code is no longer dual-licensed - only the commercial license option remains.

You can find more details here: https://neo4j.com/open-core-and-neo4j/

Original Answer:

Enterprise is available as quid-pro-quo - if you put your code out under an open source license, then you get access to the open source Neo4j Enterprise free of charge. However, if you are closed source, Neo Tech charges a license fee. This fee is determined by your needs and your ability to pay - if you are a small outfit with no venture capital, it's still free, and then the licensing cost increases as your ability to pay back to the development of Neo4j increases.

If your application is open-source as you mention, then you are free to use Neo4j Enterprise without paying for it, simply download it at neo4j.org.