Visualizing the output of a Voronoi diagram computation

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.

Here is a nice clean way to both compute and plot the Voronoi diagram with some undocumented functions:

Graphics`Region`RegionInit[];

Then:

pts = RandomReal[6, {100, 2}];

Show[GeometryPlot[VoronoiMesh[pts], Mesh -> All, 
  PlotStyle -> {Opacity[0.3], Yellow}, 
  MeshStyle -> {Darker@Green, Dashed}], Graphics[{Red, Point[pts]}]]

Now in Mathematica 10, VoronoiMesh is a standard built in function.

pts=RandomReal[{-1,1},{25,2}];
Show[VoronoiMesh[pts]
    ,Graphics[{Red,Point[pts]}]
    ,Frame-> True
]