Consider the following graph: vertices are integers between $1$ and $n,$ where $a$ is connected to $b$ if $a$ divides $b.$ This is easily constructed in Mathematica thus:
divGraph[n_] :=
With[{pairs = Subsets[Range[n], {2}]},
With[{divis = Select[pairs, Mod[#[[2]], #[[1]]] == 0 &]},
Graph[Apply[Rule, #] & /@ divis, VertexLabels -> "Name"]]]
OK, let's now look at divGraph[8]
:
You will notice that you cannot see the edge connecting $1$ to every other vertex, though we all know there should be such an edge. Is this a bug? Can it be worked around?
PS: If you are curious about why one might want to look at such a thing, see this MO question.
divGraph
:divGraph[n_] := RelationGraph[UnsameQ @ ## && Divisible[#2, #]&, Range @ n]
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