# bipartiteQuiver -- make a toric quiver on underlying bipartite graph

## Synopsis

• Usage:
bipartiteQuiver (N, M)
• Inputs:
• N, an integer, number of vertices that are sources
• M, an integer, number of vertices that are sinks
• Optional inputs:
• Flow (missing documentation) => ..., default value Canonical, specify what form of flow to use. This input can be either a string with values Canonical or Random, or else a list of integer values.
• Outputs:

## Description

This function creates the unique toric quiver whose underlying graph is the fully connected bipartite graph with N source vertices and M sink vertices.

 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 = bipartiteQuiver (2, 3, Flow=>"Random") o2 = ToricQuiver{flow => {24, 65, 71, 72, 19, 19} } 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 => {-160, -110, 96, 84, 90} o2 : ToricQuiver i3 : Q = bipartiteQuiver (2, 3, Flow=>{1, 2, 1, 3, 1, 4}) o3 = ToricQuiver{flow => {1, 2, 1, 3, 1, 4} } 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 => {-4, -8, 4, 3, 5} o3 : ToricQuiver

## For the programmer

The object bipartiteQuiver is .