# comparabilityGraph -- produces the comparability graph of a poset

## Synopsis

• Usage:
G = comparabilityGraph P
• Inputs:
• P, an instance of the type Poset,
• Outputs:
• G, an instance of the type Graph, which has an edge between two vertices if they are comparable in $P$

## Description

The comparability graph of a poset $P$ is the Graph with vertices given by the ground set of $P$ and which has edges between two vertices if they are comparable in $P$.

 i1 : comparabilityGraph booleanLattice 3 o1 = Graph{0 => {1, 2, 3, 4, 5, 6, 7}} 1 => {0, 3, 5, 7} 2 => {0, 3, 6, 7} 3 => {0, 1, 2, 7} 4 => {0, 5, 6, 7} 5 => {0, 1, 4, 7} 6 => {0, 2, 4, 7} 7 => {0, 1, 2, 3, 4, 5, 6} o1 : Graph

## Caveat

This method renames the vertices with integers $0, 1, \ldots$ corresponding to the index of the vertices in the GroundSet.