Neo4j has a self-hosted community edition that is free, though you need to update to Enterprise to expand your DB beyond one node. It's worth noting though that

Neo4j has a self-hosted community edition that is free, though you need to update to Enterprise to expand your DB beyond one node. It's worth noting though that scaling from a single node to a cluster is going to have some pretty huge performance issues whether you are using SQL or Neo4j to store your graph. The power of graph databases is that it should be very inexpensive to follow an edge in the graph but when that leads to a network hop you lose a lot of performance. If you are comfortable fitting your data onto one box, then development speed is probably more important than other factors and I would just try a few databases out and especially pay attention to how good the libraries are in your programming language of choice. Neo4j for instance had high quality libraries in Java but the experience in Python was not as good. If you have a lot of data or need next-level performance, I would start by doing some research on the various ways to store graph data and then pick a DB that supports the approach you want to take.