BFS ever failing for a unweighted and undirected graph?

Question

So I am just doing some work for my algorithms class and I was just wonder does a BFS tree ever fail on finding the single source shortest path I know that BFS finds the shortest path with the least amount of edges and I am pretty convinced BFS never fails on a unweighted graph

Ive drew multiple graphs by hand and the bfs graph and they all have turned out to be the single single source shortest path.

Answer 1

I think that BFS never fails to find the shortest path because BFS:

• assumes that all edges weight equal to 1.
• it guarantees because it processes nodes sequentially. And it means we are going to find all the vertices that are one edge away first and then all the vertices are two edge away. And then all the vertices that are three edge away and so on

Answer 2

Yeah, BFS will absolutely fail on an unweighted and undirected graph; you just have to use too much memory...