The beam size is the number of "nodes" you remember in your search. I would say when the beam size is infinity, that is you have all the nodes in graph as your size of beam then it becomes a Breadth-First-Search (BFS). On the other hand, if the beam size is 1, then it basically becomes the Depth-First-Search (DFS). The beam size is the amount of information you want to retain during the entire algorithm. The more memory/space you have the better the results but slower and vice-versa.