I actually had a friend suggest it to me and the Neo4j docs happen to be one of the many tabs I currently have open. I was already so far into using SQLite for this project and I wanted to ship it, so I decided to stick with what I had. I would be interested to see how Neo4j performs with such a big dataset (the resulting SQLite file is around 9 GB with nearly 6 million nodes and 500 billion links). I was a bit worried that Neo4j wouldn't be able to scale to a graph of that size, but that is a completely untested and ignorant opinion. If you have any experience with Neo4j, I'd love to hear your thoughts.
I've only played around with Neo4j, but it looks like Neo4j 3.0 could handle your node and edge count (although not earlier versions).
Your app likely would have been easier to write with python/Neo4j than python/SQLite due to Neo4j's query language (incidentally, Neo4j also prefers to use bidirectional BFS for shortest path, and executing the search is a very simple query similar to an SQL query). Neo4j would possibly perform better as well (I'm not sure about that, given SQLite is pretty optimized for reads).
However, as the neighboring comment states, Neo4j is quite resource-intensive. It wouldn't work on any kind of micro instance, I'm pretty sure.
Awesome job!.A great learning tool for someone coming from Non-Cs background to actually dabble with BFS Graph algorithms. After a quick search, i managed to ferret out a few implementations, one of which is this. Uses Neo4J.
https://github.com/erabug/wikigraph