  Structural convergence is a framework for convergence of graphs by
Ne\v{s}et\v{r}il and Ossona de Mendez that unifies the dense (left) graph
convergence and Benjamini-Schramm convergence. They posed a problem asking
whether for a given sequence of graphs $(G_n)$ converging to a limit $L$ and a
vertex $r$ of $L$ it is possible to find a sequence of vertices $(r_n)$ such
that $L$ rooted at $r$ is the limit of the graphs $G_n$ rooted at $r_n$. A
counterexample was found by Christofides and Kr\'{a}l', but they showed that
the statement holds for almost all vertices $r$ of $L$. We offer another
perspective to the original problem by considering the size of definable sets
to which the root $r$ belongs. We prove that if $r$ is an algebraic vertex
(i.e. belongs to a finite definable set), the sequence of roots $(r_n)$ always
exists.
