# threeVertexQuiver -- make a toric quiver on underlying graph with three vertices and a specified number of edges between each

## Synopsis

• Usage:
threeVertexQuiver E
• Inputs:
• E, a list, number of edges between each pair of vertices
• 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

 i1 : Q = threeVertexQuiver {1,2,3} o1 = ToricQuiver{flow => {1, 1, 1, 1, 1, 1} } IncidenceMatrix => | -1 -1 -1 -1 0 0 | | 1 0 0 0 -1 -1 | | 0 1 1 1 1 1 | Q0 => {0, 1, 2} Q1 => {{0, 1}, {0, 2}, {0, 2}, {0, 2}, {1, 2}, {1, 2}} weights => {-4, -1, 5} o1 : ToricQuiver i2 : Q = threeVertexQuiver ({1,2,3}, Flow=>"Random") o2 = ToricQuiver{flow => {24, 65, 71, 72, 19, 19} } IncidenceMatrix => | -1 -1 -1 -1 0 0 | | 1 0 0 0 -1 -1 | | 0 1 1 1 1 1 | Q0 => {0, 1, 2} Q1 => {{0, 1}, {0, 2}, {0, 2}, {0, 2}, {1, 2}, {1, 2}} weights => {-232, -14, 246} o2 : ToricQuiver i3 : Q = threeVertexQuiver ({1,2,3}, Flow=>{1, 2, 1, 3, 1, 4}) o3 = ToricQuiver{flow => {1, 2, 1, 3, 1, 4} } IncidenceMatrix => | -1 -1 -1 -1 0 0 | | 1 0 0 0 -1 -1 | | 0 1 1 1 1 1 | Q0 => {0, 1, 2} Q1 => {{0, 1}, {0, 2}, {0, 2}, {0, 2}, {1, 2}, {1, 2}} weights => {-7, -4, 11} o3 : ToricQuiver

## For the programmer

The object threeVertexQuiver is .