Neo4j
Neo4j is the most used open source Graph Database software at this moment.
It comes with a standard web interface.
Interaction with the database is can also be done with using a variety of software e.g.
- Java
- Python (e.g. Py2Neo package)
- R (example code here (Rneo4j package) or here (using RCurl' and 'RJSONIO'))REST client