So, if you do have data in an arbitrary graph structure and want to do a search like the Airbnb example - essentially, sort nodes by maximal total flow from a s

So, if you do have data in an arbitrary graph structure and want to do a search like the Airbnb example - essentially, sort nodes by maximal total flow from a set of starting search nodes - clearly Hopcroft-Karp isn’t appropriate, but is there an algorithm that is good for this use case? The author punts to building indices, but is there a way to express that from a graph theory perspective?