  We analyse the structure of equivalence classes of symmetric quivers whose
generating series are equal. We consider such classes constructed using the
basic operation of unlinking, which increases a size of a quiver. The existence
and features of such classes do not depend on a particular quiver but follow
from the properties of unlinking. We show that such classes include sets of
quivers assembled into permutohedra, and all quivers in a given class are
determined by one quiver of the largest size, which we call a universal quiver.
These findings generalise the previous ones for permutohedra graphs for knots.
We illustrate our results with generic examples, as well as specialisations
related to the knots-quivers correspondence.
