described by \[defn:dsqp\](c), note that the vertices are identified with the subquivers $Q^j \in {{\mathcal}{Q}^\bullet}$. We say that an admissible subquiver partition ${{\mathcal}{Q}^\bullet}$ is *ordered* if $a$ is an arrow in the contracted quiver with $ha = Q^i$ and $ta = Q^j$, then $i<j$.

Definition \[defn:dsqp\](d) can be rephrased as saying that the subquivers are ordered so that they are in “head before tail” order in contracted quiver of \[defn:dsqp\](c). Hence every admissible subquiver partition can be ordered. Figure \[fig:adm.dsqp\] provides an example. We further introduce the notation ${{\mathcal}{Q}^\bullet}_1 = {\bigcup}_{j\in[\ell]}Q^j_1$ to denote the set of arrows in $Q$ which appear in one of the $Q^j$ subquivers. Thus, the arrows of the contracted quiver described in Definition \[defn:dsqp\](c) are identified with $Q_1\setminus {{\mathcal}{Q}^\bullet}_1$.

\(00) at (0,0) [$\bullet$]{}; (10) at (1,0) [$\bullet$]{}; (20) at (2,0) [$\bullet$]{}; (21) at (2,1) [$\bullet$]{}; (30) at (3,0) [$\bullet$]{}; (31) at (3,1) [$\bullet$]{}; (40) at (4,0) [$\bullet$]{}; (41) at (4,1) [$\bullet$]{};

\(10) – (00); (10) – (20); (10) – (21); (21) – (31); (20) – (30); (31) – (30); (40) – (30); (40) – (41);

(-.25,0) – (-.25,.25) – (1,.25) – (2,1.25) – (2.25,.95) – (1.5,.25) – (2.25,.25) – (2.25,-.25) – (-.25,-.25) – (-.25,0) ; (2.75, 