Can you use neo4j to store weighted graphs? Looking at their api it doesn't seem like there's any way to specify edge weights (or any other metadata about edges).
You can set properties (including weights, though not sure if you can define said weights in a tightly integrated manner - they're just an additional property) on nodes and edges ("relationships"). It's right there in the getting started guide's "Create a small graph" section:
Please let me know if you find anything that can handle negative edge weights well while efficiently tracking shortest paths. I've found some papers with efficient implementations for frequently updated edge weights, but haven't found anything implemented or accessible.
http://wiki.neo4j.org/content/Getting_Started_Guide#Create_a...
Weights are treated like any other metadata.