>>11594994If your graph is stored in a dcel or a quadcel you can use the orbit operator (I implemented it on uni once, don't really remember how it goes exactly, but I think you take the dual of an edge, move forward and take duals again). By repeating this operator you get the entire orbit with all the adjacent vertexes.
If you're using an adjacency list, a bredth first search should do it. The same works on an adjacency matrix.