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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]:

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.

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  • 2
    $\begingroup$ Which edge is missing (besides 1$\to$1)? $\endgroup$ – John Joseph M. Carrasco Sep 12 '17 at 23:45
  • $\begingroup$ Yeah.... What's the problem? $\endgroup$ – David G. Stork Sep 13 '17 at 0:45
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    $\begingroup$ an alternative way to define divGraph : divGraph[n_] := RelationGraph[UnsameQ @ ## && Divisible[#2, #]&, Range @ n] $\endgroup$ – kglr Sep 13 '17 at 1:28
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I'm not sure what edges you're having trouble seeing.

To highlight the edges connecting 1 to everyone else you can use Highlight.

divGraph[8]~ HighlightGraph ~ (1 -> # & /@ Range[2, 8])

enter image description here

Maybe you'll like the layout better of:

Graph[divGraph[8], GraphLayout -> "RadialDrawing"] // 
 HighlightGraph[#, 1 -> # & /@ Range[2, 8]] &

enter image description here

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  • 1
    $\begingroup$ Hmm. Perhaps temporary blindness, but on the other hand, the radial drawing looks way better, so I am glad I asked! $\endgroup$ – Igor Rivin Sep 13 '17 at 0:58

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