The official website for The Settlers of Catan

Question about Base Game Longest Road - Can a continuous road be circular?

Answer

In principle, yes; but on Catan the circle is a hexagon. When counting the individual road pieces, it doesn’t matter whether or not they are built in a more or less straight line - what matters is that they establish an uninterrupted connection between two intersections. This is why 6 road pieces connected in a hexagonal fashion still count as 6 road pieces.