In Mathematica. When using images as vertices in GraphPlot, how do I prevent images from overlapping?

Question

I am using GraphPlot to draw directed graphs with roughly a 100 vertices. I am replacing each vertex with a small rectangular or square image by defining the VertexRenderingFunction. The images often overlap. Is there a way to get Mathematica to space the vertices further apart to prevent them from overlapping?

I have tried the various obvious options for 'Method' ("SpringElectricalEmbedding", "SpringEmbedding", "HighDimensionalEmbedding", "CircularEmbedding", "RandomEmbedding", "LinearEmbedding").

trans = {1 -> 1, 2 -> 1, 3 -> 1, 4 -> 1, 5 -> 1, 6 -> 1, 7 -> 1,
8 -> 1, 9 -> 1, 10 -> 1, 11 -> 1, 12 -> 1, 13 -> 1, 14 -> 1, 
15 -> 1, 16 -> 1, 17 -> 1, 18 -> 13, 19 -> 1, 20 -> 13, 21 -> 13, 
22 -> 70, 23 -> 1, 24 -> 1, 25 -> 1, 26 -> 1, 27 -> 13, 28 -> 13, 
29 -> 1, 30 -> 13, 31 -> 13, 32 -> 1, 33 -> 19, 34 -> 70, 35 -> 70,
36 -> 1, 37 -> 1, 38 -> 1, 39 -> 39, 40 -> 13, 41 -> 2, 42 -> 13, 
43 -> 1, 44 -> 2, 45 -> 1, 46 -> 52, 47 -> 2, 48 -> 68, 49 -> 49, 
50 -> 19, 51 -> 78, 52 -> 1, 53 -> 1, 54 -> 39, 55 -> 13, 56 -> 56,
57 -> 13, 58 -> 13, 59 -> 1, 60 -> 36, 61 -> 1, 62 -> 52, 63 -> 2,
6 4 -> 68, 65 -> 19, 66 -> 56, 67 -> 4, 68 -> 76, 69 -> 19, 
70 -> 78, 71 -> 1, 72 -> 39, 73 -> 52, 74 -> 56, 75 -> 23, 
76 -> 76, 77 -> 56, 78 -> 78};

image = {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}};

GraphPlot[trans, DirectedEdges -> True, VertexLabeling -> True,
VertexRenderingFunction -> (Inset[
ArrayPlot[image, ImageSize -> 15, Mesh -> True], #1] &)]

Answer 1

Edit [I started over, based on the example you gave]:

Using your trans and image you could try:

p = ArrayPlot[image, ImageSize -> 35, Mesh -> True];

Graph[trans, DirectedEdges -> True,  VertexLabels -> Placed[p, Tooltip], 
  ImagePadding -> 10, ImageSize -> 500]

The images will appear in tooltips when you mouse over each vertex. You could use different images for different vertex labels if you wish; just use a list of rules.

The picture below shows what it looks like (without the tooltips). Click on link to see how it works with tooltips.