I have two loosely related questions about SetProperty and VertexSize:

Suppose we have a largeish graph:
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.)

2. How can I set the VertexSize when using a predefined graph style?  For example the following doesn't work: