How to Apply Hierarchical Edge Bundling in a Very Large Graph

Question

I have a directed graph consisting of 1616 vertices and an edge count = 3315. I'm trying to plot this by the code...

Clear["Global`*"]
SetSystemOptions[
  "GraphOptions" -> {"CacheResults" -> True, 
    "EdgeCountThreshold" -> 20000, "RenderingOrder" -> "VertexFirst", 
    "VertexCountThreshold" -> 2000}];

x = N6037; y = N6065 | N6071 | N6073; g = 
 Graph[edges, VertexLabels -> {x | y -> Automatic}, 
  VertexStyle -> {White, x | y -> Red}, 
  VertexSize -> {5, x | y -> 10}, 
  VertexLabelStyle -> {x | y -> Directive[Bold, Black, 20]}, 
  EdgeStyle -> {GrayLevel[0.75]}, 
  GraphLayout -> {"EdgeLayout" -> "HierarchicalEdgeBundling"}, 
  BaseStyle -> {Arrowheads -> 0.04}]

Unfortunately, all I get is a graphics object for output:

The best I can do is to run

SimpleGraph[g]

and that does produce this output

But it seems that my code to color each of the 4 labeled vertices RED is not working; nor is my code to reduce the sizes of the arrows pointing into the circle's edge. Yet, my code for VertexLabelStyle is working.

Mentioned above, there are 1616 vertices. For this reason, I felt it is too large to include in this post; that is, in my code I have edges = {the set of 3315 directed edges}.

The labeled vertices N6065, N6037, N6073, and N6071 are vertices in the edges = {the set of 3315 directed edges} that I want to color RED, to make these 4 RED nodes larger than the others so they standout, and to control (reduce) the size of the arrows.

This is my first time trying the Hierarchical Edge Bundling feature. I have already review other posts on this topic. Any and all suggestions are most appreciated!!

Answer 1

For large graph, drawing code uses Point for vertex shape at default. You could specify PointSize to control vertex size and Arrowheads seems works fine:

Graph[edges, VertexLabels -> {x | y -> Automatic}, 
 VertexStyle -> {White, 
   x | y -> Directive[Red, AbsolutePointSize[5]]}, 
 VertexLabelStyle -> {x | y -> Directive[Bold, Black, 20]}, 
 EdgeStyle -> {GrayLevel[0.75]}, 
 GraphLayout -> {"EdgeLayout" -> "HierarchicalEdgeBundling"}, 
 BaseStyle -> {Arrowheads -> 0.01}]