Using SetPropery and VertexSize

Questions
,
1

I have two loosely related questions about SetProperty and VertexSize:

Suppose we have a largeish graph:

g=RandomGraph[BarabasiAlbertGraphDistribution[100,1]]
  1. Why does SetProperty[g, VertexSize → Large] make the vertices smaller than default instead of larger? This is a bit counterintuitive. I can work around it by specifying a number, e.g. VertexSize → 10. However, the actual size will still depend on the size of the graph (if we have a graph with 1000 nodes instead of 100, it’ll be different).

What I’m aiming for is setting the vertex size in a general way so that it’ll be a reasonable factor bigger than the default regardless of the size of the graph. The application is highlighting a particular vertex, e.g. SetProperty[g, VertexSize → {10 → Large}]. I don’t know how to choose a vertex size value that’ll work for a graph of any size. For example making the highlighted vertex precisely twice bigger than the rest would probably work well.

(I know I can highlight by colouring, but this is in addition to that.)

  1. How can I set the VertexSize when using a predefined graph style? For example the following doesn’t work:
SetProperty[
 RandomGraph[BarabasiAlbertGraphDistribution[100, 1], 
  GraphStyle -> "LargeNetwork"],
 VertexSize -> {10 -> 5}
 ]
2

Consider a not-styled graph:

g = RandomGraph[BarabasiAlbertGraphDistribution[100, 1]]

440×344 11.1 KB

Change all vertex sizes relatively to plot diagonal

SetProperty[g, VertexSize -> {"Scaled", .02}]

433×340 11.8 KB

Change single vertex color and size relatively to plot diagonal

SetProperty[g, {VertexSize -> {10 -> {"Scaled", .04}},  VertexStyle -> {10 -> Red}}]

433×339 11.4 KB

Now consider styled graph

h = RandomGraph[BarabasiAlbertGraphDistribution[100, 1], GraphStyle -> "LargeNetwork"]

453×259 9.54 KB

Change single vertex size relatively to plot diagonal

SetProperty[h, {VertexShapeFunction -> {10 -> "Circle"}, VertexSize -> {10 -> {"Scaled", .04}}}]

445×258 9.57 KB

Use another method and add color

SetProperty[h, VertexStyle -> {10 -> {Red, PointSize[.04]}}]

449×257 9.8 KB

3

Great tips Vitaliy, I don’t know how I could have missed some of those basic options (probably too sleepy when posting). I tried VertexSize → Scaled[…] but it typically gives ellipses instead of circles becaues the plot aspect ratio is not square.