I've actually been working on an extension to perform breadth first search queries in SQLite on general graphs [0]. The extension is actually based off of the transitive closure extension. You can use it on any existing SQLite database as long as you can wrangle your edges into a single table (real or virtual) and the node ids are integers (I'm planning on removing this constraint in the future).
[0]: https://github.com/abetlen/sqlite3-bfsvtab-ext