Mathematica Code
This code needs the DiscreteMath` module to be loaded.
points = Table[Random[], {100}, {2}]
PlanarGraphPlot[points,
LabelPoints -> False]
Points Used
As random points were used, here are the points for this particular diagram:
{{0.939718, 0.00149083}, {0.459635, 0.328918}, {0.545203, 0.521633},
{0.142404, 0.982294}, {0.733818, 0.0352899}, {0.150613, 0.903548},
{0.636916, 0.557598}, {0.0998009, 0.48953}, {0.424942, 0.925505},
{0.441789, 0.623109}, {0.40419, 0.765702}, {0.472585, 0.453032},
{0.464472, 0.764211}, {0.0129508, 0.124114}, {0.919269, 0.242578},
{0.870547, 0.14182}, {0.185451, 0.207288}, {0.719935, 0.238272},
{0.548535, 0.64969}, {0.620134, 0.748742}, {0.123593, 0.724185},
{0.178345, 0.125632}, {0.719403, 0.958484}, {0.705759, 0.6726},
{0.254932, 0.194273}, {0.692809, 0.548486}, {0.335663, 0.951695},
{0.822261, 0.406666}, {0.150212, 0.744407}, {0.102327, 0.168394},
{0.601678, 0.0947169}, {0.482193, 0.419652}, {0.478085, 0.370531},
{0.303848, 0.29402}, {0.758682, 0.412048}, {0.598089, 0.62142},
{0.50375, 0.217775}, {0.90528, 0.0729336}, {0.168087, 0.26608},
{0.0830191, 0.666267}, {0.0178743, 0.521673}, {0.980692, 0.497873},
{0.416196, 0.426957}, {0.498499, 0.078221}, {0.938112, 0.0564251},
{0.194651, 0.784201}, {0.17943, 0.644377}, {0.596562, 0.162781},
{0.67568, 0.426602}, {0.691281, 0.0898479}, {0.507594, 0.160522},
{0.608262, 0.42358}, {0.489719, 0.638848}, {0.62757, 0.925707},
{0.0735229, 0.211892}, {0.129071, 0.847486}, {0.135411, 0.155467},
{0.93442, 0.0632851}, {0.955981, 0.511089}, {0.337858, 0.900504},
{0.280301, 0.0844871}, {0.646577, 0.810656}, {0.772707, 0.923965},
{0.0383153, 0.387075}, {0.282988, 0.285117}, {0.410746, 0.461368},
{0.209465, 0.0732255}, {0.281675, 0.613882}, {0.0740536, 0.917759},
{0.347255, 0.550597}, {0.118073, 0.40667}, {0.0093963, 0.650093},
{0.837772, 0.322183}, {0.362819, 0.839438}, {0.065065, 0.398217},
{0.324504, 0.452362}, {0.782077, 0.1131}, {0.913758, 0.990994},
{0.572613, 0.0398746}, {0.632083, 0.377112}, {0.498559, 0.122116},
{0.284828, 0.826515}, {0.380486, 0.715446}, {0.275432, 0.176422},
{0.542714, 0.393263}, {0.912613, 0.336984}, {0.477649, 0.995046},
{0.58811, 0.884622}, {0.695572, 0.881946}, {0.674352, 0.893628},
{0.122959, 0.842071}, {0.0422684, 0.516516}, {0.6244, 0.719956},
{0.75744, 0.690001}, {0.243914, 0.00450979}, {0.482008, 0.513579},
{0.7012, 0.611247}, {0.569394, 0.176595}, {0.223551, 0.616201},
{0.981285, 0.291973}}