VertexSize doesn't scale with Graph layout?

I wonder about how I could make a Graph scale automatically when I vary the size of the vertices.

I would like to visualize information with a Graph. The vertices all have e.g. additional info like a weight which I would like to visualize with the vertices drawn with different sizes.

However, when I define the sizes, the graph keeps the original (as opposed to the new) layout. The graph then becomes invisible.

Graph[{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 3,3 \[UndirectedEdge] 1, 3 \[UndirectedEdge] 4}]

shows:

Now I add the "weight"

Graph[{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 3,3 \[UndirectedEdge] 1, 3 \[UndirectedEdge] 4},VertexSize -> {1 -> 1.1, 2 -> 1.2, 3 -> 1.3, 4 -> 1.4}]

This shows:

What I would like is that the Graph would be like

Any thoughts?

This is a graph currently working on. As you can see one vertex hits his neighbour. I would expect MM to or reposition this vertex a bit further or to scale down all nodes. Of course this can be done by dividing the vertexes by a number. But this is manual work to see what looks best. I hope there is another way.

Answer

Does the following do what you want?

WeightedGraph[edges_, weights_, options___]:=
  Block[{maxweight=Max[#[[2]]&/@weights]},
    Graph[edges,VertexSize->((#[[1]]->0.9*#[[2]]/maxweight)&/@weights),options]]


WeightedGraph[{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 3,
               3 \[UndirectedEdge] 1, 3 \[UndirectedEdge] 4},
   (*weights:*) {1 -> 1.1, 2 -> 1.2, 3 -> 1.3, 4 -> 1.4}]

The second line is basically your Graph call, except that it uses WeightedGraph instead of Graph, and the weights don't have VertexSize-> in front of them.