Hasse Diagram

Author

Eric W. Weisstein
March 7, 2017

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/HasseDiagram.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/HasseDiagram.html.

©2017 Wolfram Research, Inc. except for portions noted otherwise

Graphic

<<Combinatorica`

Undirected

gopts=Sequence[VertexSize->{"Scaled",.05},System`EdgeStyle->Black,System`VertexStyle->Red];

GraphicsRow[hasse=CombinatoricaGraphToV8Graph[#,gopts]&/@BooleanAlgebra/@Range[2,5]]

ToEntity/@hasse

See Skienna and Pemmaraju, p. 30

Directed

gs=Table[MakeGraph[Subsets[n],((Intersection[#2,#1]===#1)&&(#1≠#2))&],{n,2,5}];

GraphicsGrid[{
CombinatoricaGraphToV8Graph[#,gopts,VertexCoordinates->Automatic,GraphLayout->"SpringElectricalEmbedding",EdgeShapeFunction->GraphElementData["FilledArcArrow","ArrowSize"->0.1]]&/@gs,CombinatoricaGraphToV8Graph[#,gopts]&/@HasseDiagram/@gs
},ImageSize->400]