A Hasse diagram generated in Mathematica.

It’s that time of year again; the new students have started at DIKU and start their careers as computer science students with the course DiMS — Discrete Mathematical Structures, taught from the book by the same name.

Part of the curriculum is learning about Hasse diagrams, which in essence are a way of easily visualizing the relationships between different elements under a partial order.

Now, a student came and asked me about how to draw these diagrams in Mathematica, so I got some code working which did just that. The resulting diagram, is the picture used for this post.

In the spirit of sharing, here is the Mathematica-code I used to generate this picture:

(* Combinatorica contains HasseDiagram,so we need to load it. *)
<

(* The set the partial order operates on. *)
nums = {1, 2, 4, 7, 8, 14, 30};

(* Define our partial order. *)
pOrder[x_, y_] := Divisible[y, x];

(* Generate a directed graph from the partial order. *)
g = MakeGraph[nums, pOrder];

(* Now create our Hasse diagram *)
h = HasseDiagram[g];

(* Finally, let's see the resulting graph. *)
ShowGraph[h, VertexStyle -> PointSize[0.05], VertexLabel -> True,
VertexLabelColor -> White, VertexLabelPosition -> {0.012, 0}]