  We study cluster algebras arising from cluster tubes. We obtain categorical
interpretations for $g$-vectors, $c$-vectors and denominator vectors for
cluster algebras of type $\mathrm{C}$ with respect to arbitrary initial seeds.
In particular, a denominator theorem has been proved, which enables us to
establish the linearly independence of denominator vectors of cluster variables
from the same cluster for cluster algebras of type
$\mathrm{A}\mathrm{B}\mathrm{C}$. This strengthens the link between cluster
tubes and cluster algebras of type $\mathrm{C}$ initiated by Buan, Marsh and
Vatne.
