# subquiver representation

There are many ways to take a subset $R=(R_0,R_1)$ of a quiver $Q=(Q_0,Q_1)$. This is because we can consider $R_0\subset Q_0$ and $R_1\subset Q_1$. Alternatively, $R$ is itself a quiver, with $|R_1|$ arrows and $|R_0|$ vertices. Thus we can also consider $R$ independently of the arrow/vertex labeling of $Q$.

The two methods corresponding to these ideas are referenced in the examples below.

 i1 : Q = bipartiteQuiver(2, 3) o1 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1} } IncidenceMatrix => | -1 -1 -1 0 0 0 | | 0 0 0 -1 -1 -1 | | 1 0 0 1 0 0 | | 0 1 0 0 1 0 | | 0 0 1 0 0 1 | Q0 => {0, 1, 2, 3, 4} Q1 => {{0, 2}, {0, 3}, {0, 4}, {1, 2}, {1, 3}, {1, 4}} weights => {-3, -3, 2, 2, 2} o1 : ToricQuiver i2 : Q_{0,1,3} o2 = ToricQuiver{flow => {1, 1, 1} } IncidenceMatrix => | -1 -1 0 | | 0 0 -1 | | 1 0 1 | | 0 1 0 | Q0 => {0, 1, 2, 3} Q1 => {{0, 2}, {0, 3}, {1, 2}} weights => {-2, -1, 2, 1} o2 : ToricQuiver i3 : Q^{0,1,3} o3 = ToricQuiver{flow => {1, 1, 0, 1, 0, 0} } IncidenceMatrix => | -1 -1 -1 0 0 0 | | 0 0 0 -1 -1 -1 | | 1 0 0 1 0 0 | | 0 1 0 0 1 0 | | 0 0 1 0 0 1 | Q0 => {0, 1, 2, 3, 4} Q1 => {{0, 2}, {0, 3}, {0, 4}, {1, 2}, {1, 3}, {1, 4}} weights => {-2, -1, 2, 1, 0} o3 : ToricQuiver