  We give necessary and sufficient condition that an element of an arbitrary
$C^{*}$-algebra is an isolated vertex of the orthograph related to the mutual
strong Birkhoff-James orthogonality. Also, we prove that for all
$C^{*}$-algebras except $\mathbb{C},\mathbb{C}\oplus\mathbb{C}$ and
$M_2(\mathbb{C})$ all non isolated points make a single connected component of
the orthograph which diameter is less than or equal to $4$, i.e. any two non
isolated points can be connected by a path with at most $4$ edges. Some related
results are given.
