$B(r)$ expands to $B(s)$ in the annulus, we take distinguished elements to form the set $$\Sigma(A(r,s)) \coloneqq \{ \rho_{B(t)} : r < \log t < s \}.$$ This is called the *skeleton* of $A(r,s)$.

The annulus $A(r,s)$ canonically retracts onto $\Sigma(A(r,s))$ via $$\tau \colon {\left\lvert \cdot \right\rvert}_x \longmapsto \rho_{B(\log |T|_x)}.$$ Berkovich showed that this is a strong deformation retraction [@Berk Proposition 4.1.6].

For a smooth, projective curve $X/K$, a *semistable vertex set* $V$ of $X$ is a finite set of type II points in ${X^{\rm an}}$ such that ${X^{\rm an}}\setminus V$ is (isomorphic to) a disjoint union of finitely many open annuli and infinitely many open discs. Semistable vertex sets always exist [@BPR13 Proposition 4.22]. If $\chi(X) \le 0$, then a unique minimal skeleton exists \[*loc. cit.*, Corollary 4.23\].

Given a semistable vertex set $V$ of $X$, the associated (finite) *skeleton* is $$\Sigma(V) \coloneqq V \bigcup \Sigma(A)$$ where the union is over the finite set of open annuli of ${X^{\rm an}}\setminus V$. There is a canonical retraction $\tau_V \colon {X^{\rm an}}\to \Sigma(V)$ which is, in fact, a strong deformation retraction.

$\Sigma(V)$ is a $\Lambda$-rational metric graph with a canonical graph model $(V, E)$. The edges of $\Sigma(V)$ are $\Sigma(A)$ for 