Agree re "depends a lot on specific question", but the problem you specified still sounds very much like BFS, especially "shortest path" part.
My assumption for the Facebook graph would be that there is basically no way we can traverse it all, so your only hope is to find the path without expanding all the nodes. DFS will not work for that at all, but both BFS and IDFS may give you practical results.
This leaves the question of BFS vs IDFS, and that depends heavily on the details of the problem. For example, if the graph is already in RAM, then IDFS would be the best. But if the graph is not already in RAM, and you have to fetch it (from database or remote API), you'd definitely want the caching between successful IDFS rounds. And if you do that, then you might as well do BFS -- approximately the same memory performance, and much easier code.
As for usage, while BFS itself is not used this much, it's more advanced versions, Dijkstra and A*, are used all the time in graph traversals. For example, in many computer games, navigation apps and robotics planners.
(And back to original topic: if we had conversation like this during the interview, then you would likely get good score from me, even if I was fully convinced that BFS is the only way to go. After all, I am not testing for the specific bot of trivia -- I am testing for the ability to reason about algorithms)
My assumption for the Facebook graph would be that there is basically no way we can traverse it all, so your only hope is to find the path without expanding all the nodes. DFS will not work for that at all, but both BFS and IDFS may give you practical results.
This leaves the question of BFS vs IDFS, and that depends heavily on the details of the problem. For example, if the graph is already in RAM, then IDFS would be the best. But if the graph is not already in RAM, and you have to fetch it (from database or remote API), you'd definitely want the caching between successful IDFS rounds. And if you do that, then you might as well do BFS -- approximately the same memory performance, and much easier code.
As for usage, while BFS itself is not used this much, it's more advanced versions, Dijkstra and A*, are used all the time in graph traversals. For example, in many computer games, navigation apps and robotics planners.
(And back to original topic: if we had conversation like this during the interview, then you would likely get good score from me, even if I was fully convinced that BFS is the only way to go. After all, I am not testing for the specific bot of trivia -- I am testing for the ability to reason about algorithms)