  A path connected subanalytic subset in $\mathbb{R}^n$ is naturally equipped
with two metrics, the inner and the outer metrics. We say that such a subset is
Lipschitz normally embedded (LNE) if these two metrics are equivalent. In this
article we give some criteria for a subanalytic set to be LNE. We introduce a
new notion called link Lipschitz normally embedded and we prove that this
notion is equivalent to LNE notion in the case of sets with connected links and
we present some applications of it and, in particular, we prove that the LNE
property is a conical property. Some examples are also presented.
