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I worked out how (one way...) to import a .dot graph format file into Mathematica using

Import["/home/username/Desktop/mygraph.dot"]

which works a treat, drawing a nice graph with vertices and edges all joined up.

But can anyone please explain how I can make the vertex labels either bigger, or add a coloured background to the label text?

I have many edges between vertices and as it is the thin black small text is difficult to read.

Thanks

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You can add Graphoptions during Importing. That is, if example.dot is the file to be imported

Export["example.dot", Import["ExampleData/sample.gv"], "DOT"]

"example.dot"

you can import it as follows

Import["example.dot", ImagePadding -> 20, ImageSize -> 400, 
  VertexLabelStyle -> 16, EdgeStyle -> Directive[Red, Thick]] 

to get

enter image description here

This feature is documented in DOT >> Options:

enter image description here

Alternatively, if you already imported the graph, you can use SetProperty to make changes in any of the Graph options:

g2 = Import["example.dot"]

enter image description here

SetProperty[g2, {VertexLabelStyle -> 16, EdgeStyle -> Directive[Red, Thick], 
  ImageSize -> 400, ImagePadding -> 30}]

enter image description here

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