I don't actually use a graph database. In the past I tried neo4j and memgraph (similar but in memory), and both were just too slow. So I builder my own database, specifically designed for the operations I needed to make generating and updating random walks very fast. This allowed to lower the execution time of pagerank by a factor of 100x compared to traditional algorithms.
For the search, I use my other SQLite database to do a full text search for the profiles. Then I rank these profiles using Pagerank, and I create a composite rank which is a combination of search similarity, and reputation. The result is what is powering npub.world