graphics - Visualizing the output of a Voronoi diagram computation

I need to plot a graph (to be specific: Fortune Algorithm output) with given vertex coordinates and a few unconnected vertices. I am thinking of using Mathematica for that.

GraphPlot does much of the task with VertexCordinateRules option but does not plot unconnected points.

1. 
   

   So is there any way to do this?
   And it would be even nicer if that graph comes with 2-D Axes. I was thinking to use ListLinePlot and Point commands but they give two different graphs as output.

   
   


2. 
   

   Is there any option for combining output from two graphs? (The Show command didn't help.)

   
   

Answer

I didn't quite follow the description of your graph, but are you aware of this functionality?:

data = MapIndexed[Flatten[{##}] &, RandomReal[1, {100, 2}]];

ListDensityPlot[
 data,
 InterpolationOrder -> 0,
 ColorFunction -> Hue,
 Mesh -> All,
 Epilog -> Point@data[[All, {1, 2}]]
]

Specifically note InterpolationOrder -> 0.