Graphs and Degrees · Medium problem

Nine friends sit evenly spaced around a circular table, numbered $1$ to $9$ in order around the circle. Draw an edge between two friends whenever the shorter way around the table between their seats passes exactly $1$ or exactly $2$ other... no other seats, i.e. they are $1$ or $2$ seats apart (so seat $9$ is $1$ seat from seat $1$, and $2$ seats from seat $2$). How many edges does this “close neighbors” graph have?