Some problems do not give you a graph with explicit nodes and edges.
Instead, they describe states and transitions. These are implicit graphs. Each state is a node. Two states are connected if you can transition from one to the other in one step. You do not build an adjacency list. You generate neighbors on the fly by applying the allowed transitions.
BFS works the same way: start at the initial state, explore all reachable states one step away, then two steps away, and so on. Problems like Word Ladder, Sliding Puzzle, and Knight's Shortest Path use implicit graphs.