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