A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point is drawn for each element of the poset, and line segments are drawn between these points according to the following two rules:
1. If 
in the poset, then the point corresponding to 
appears lower in the drawing than the point corresponding
to 
.
2. The line segment between the points corresponding to any two elements 
and 
of the poset is included in the drawing iff 
covers 
or 
covers 
.
Hasse diagrams are also called upward drawings.
Hasse diagrams for a graph 
are implemented as HasseDiagram[g]
in the Wolfram Language package Combinatorica`
, where 
is a directed acyclic Combinatorica graph object. They may be implemented
in a future version of the Wolfram Language
as HasseGraph.
The above figures show the Hasse diagrams for Boolean algebras of orders 
,
3, 4, and 5. In particular, these figures illustrate the partition between left and
right halves of the lattice, each of which is the Boolean
algebra on 
elements (Skiena 1990, pp. 169-170). These correspond precisely to the hypercube
graphs 
.
