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I have a problem with Graph plot scaling of vertex sizes when I go from 999 vertices to 1000 vertices. The following code scales the vertex size properly when the numNodes = 999; but not numNodes = 1000. Very strange like something goes haywire in plotting graphs 1000 nodes or larger.

ClearAll["Global`*"];
(* Define some utility functions *)
addVertices[G_, numVertices_] := (
  GN = G;
  vc = VertexCount[GN];
  (* Preferential Attachment Part A *)
  For[i = 1, i <= numVertices, i++,
   (* Preferential Attachment Part A Barabasi / Albert Method *)
   (* The rich get richer... *)
   GN = EdgeAdd[
     GN, (vc + i) \[UndirectedEdge] RandomChoice[GraphCenter[GN]]];
   (* Preferential Attachment Experiment 1 *)
   GN = EdgeAdd[
     GN, (vc + i) \[UndirectedEdge] RandomChoice[GraphPriphery[GN]]];
   ];
  Return[Graph[GN, VertexLabels -> Automatic, 
    PlotLabel -> "New G with additional vertices"]]
  )
If[$KernelCount < 1, LaunchKernels[]];
Framed[Style[
  StringJoin["Running [", ToString[$KernelCount], "] kernels"]], 
 Background -> LightBlue]
numNodes = 1000;
m = 2; (* Parameter of attachment *)
G = Graph[RandomGraph[BarabasiAlbertGraphDistribution[numNodes, m]], 
  VertexStyle -> White];
vcount = VertexCount[G];
heatIndex = Table[VertexDegree[G, i], {i, 1, vcount}] ;
Length[Range[Max[heatIndex]]];
tempRange = Table[ColorData["TemperatureMap"][r], {r, 0., 1., 1/%}];
tempDegree = Table[tempRange[[heatIndex[[i]]]], {i, 1, vcount}];
vs = Table[i -> tempDegree[[i]], {i, 1, vcount}];
vh = Table[
   i -> (Log[numNodes]*m*heatIndex[[i]])/(Max[heatIndex]), {i, 1, 
    vcount}];
pl = Style[
   StringJoin[
    "Heat/Size Map of Random Barabasi/Albert Graph\nO(V) = ", 
    ToString[numNodes], ", Diameter G = ", ToString[GraphDiameter[G]],
     ", m = ", ToString[m]], Bold, FontFamily -> "Comic Sans MS"];
G = Graph[G, VertexStyle -> vs, VertexSize -> vh, PlotLabel -> pl];
vd = Thread[VertexList@G -> Normalize[VertexDegree@G, Total]]*
    Log[VertexDegree@G] // N;
G2 = SetProperty[G, VertexSize -> vd]`

See the following for additional backup material. Vertex sizes scaled by vertex degree?

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1 Answer 1

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You could set up VertexShapeFunction -> "Circle".

SetProperty[G, {VertexSize -> vd, VertexShapeFunction -> "Circle"}]
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  • $\begingroup$ That worked. I am not sure why, perhaps you could explain it. Is there a way to add a black border to the circle? $\endgroup$
    – Phillip D. Neumiller
    Jun 22 at 17:35
  • $\begingroup$ @PhillipD.Neumiller It's caused by automatic large plot theme. You could add EdgeForm to vertex styles : vs = Table[ i -> Directive[EdgeForm[Black], tempDegree[[i]]], {i, 1, vcount}] $\endgroup$
    – halmir
    Jun 23 at 14:55

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