  Let $G$ be a graph. Its laplacian matrix $L(G)$ is positive and we consider
eigenvectors of its first non-null eigenvalue that are called Fiedler vector.
They have been intensively used in spectral partitioning problems due to their
good empirical properties. More recently Fiedler vectors have been also
popularized in the computer graphics community to describe elongation of
shapes. In more technical terms, authors have conjectured that extrema of
Fiedler vectors can yield the diameter of a graph. In this work we present
(FED) property for a graph $G$, i.e. the fact that diameter of a graph can be
obtain by Fiedler vectors. We study in detail a parametric family of trees that
gives indeed a counter example for the previous conjecture but reveals a
threshold phenomenon for (FED) property. We end by an exhaustive enumeration of
trees with at most 20 vertices for which (FED) is true and some perspectives.
