co.combinatorics - Is the graph of a thresholded correlation matrix chordal?

It was described in this previous question how to obtain a correlation matrix whose entries come from the scalar product of certain vectors $u_1, u_2, dots,u_n$. If we let the vectors be $$u_i=(1, cos(frac{2pi i}{n}), sin(frac{2pi i}{n}),0,dots, 0)$$ we can set a high enough threshold so that the corresponding graph is a cycle of length $n$ and thus not chordal.