Sampling in large graph using simple random walk
While the algorithm doesn't know the graph, when you are analyzing the performance of the algorithm on a graph, you do know the graph.

For a similar example, take the egg dropping puzzle. In this puzzle, the algorithm doesn't know the value of $T$, but when analyzing the algorithm, you are allowed to use the value of $T$; indeed, otherwise it's not clear how you'd ever end up with a running time depending on $T$.