I have implemented an algorithm to calculate vertex normals by taking the normalized average of all its adjacent triangles. I have subdivided a cube two times with catmull clark and checked the shading. If you look close at the first image you can have these dark lines than run along the topological edges of the mesh (defined in the second picture).
Is this normal (no pun intented) and have to do with vertex normals being just an approximation of surface normals? If so why exactly does these artifacts occur? Or have I probably done something wrong with how I calculated the normals?