Consider a not-styled graph:
g = RandomGraph[BarabasiAlbertGraphDistribution[100, 1]]
![](http://i.imgur.com/ya5yyRi.png)
Change all vertex sizes relatively to plot diagonal
SetProperty[g, VertexSize -> {"Scaled", .02}]
![](http://i.imgur.com/63EavYX.png)
Change single vertex color and size relatively to plot diagonal
SetProperty[g, {VertexSize -> {10 -> {"Scaled", .04}}, VertexStyle -> {10 -> Red}}]
![](http://i.imgur.com/dnrWDam.png)
Now consider styled graph
h = RandomGraph[BarabasiAlbertGraphDistribution[100, 1], GraphStyle -> "LargeNetwork"]
![](http://i.imgur.com/ucDHCPn.png)
Change single vertex size relatively to plot diagonal
SetProperty[h, {VertexShapeFunction -> {10 -> "Circle"}, VertexSize -> {10 -> {"Scaled", .04}}}]
![](http://i.imgur.com/0MQFPWH.png)
Use another method and add color
SetProperty[h, VertexStyle -> {10 -> {Red, PointSize[.04]}}]