1
$\begingroup$

Given vectors $V$ of length $d$, construct a graph $G = (V, E)$ where $\{u, v\} \in E$ iff the Pearson correlation between $u$ and $v$ is larger than some threshold $t > 0$. Is $G$ chordal? It seems like it should be, because a long chordless cycle like $a$ correlates with $b$, $b$ with $c$, $c$ with $d$ but nothing else seems difficult to construct. However, I cannot find a simple proof or a reference.

$\endgroup$
2
$\begingroup$

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 $$u_i=(1, \cos(\frac{2\pi i}{n}), \sin(\frac{2\pi i}{n}),0,\dots, 0)$$ we can set a high enough threshold so that the corresponding graph is a cycle of length $n$ and thus not chordal.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.