Finite-component conjecture for global hot spots

Let $amma$ be a metric graph satisfying the standing assumptions of the paper. Let $M$ denote the set of all global maxima and minima of second eigenfunctions on $amma$.

Finite-component conjecture. The set $M$ always has finitely many connected components; in particular, it is either finite or uncountable.

The conjecture concerns the global analogue of the already established finite-or-uncountable dichotomy for the set of all possible local extrema. The source gives no resolution status.