We present here a simple program to generate a variety of random graphs with a variable number of vertices and edges and Random edge weights, either directed or undirected. You can put an insane number of vertices in and it will run ... but it will take a while...
If you want the Random graph to be directed you can change the DirectedEdges-> parameter in the RandomGraph function. Also if you want a different number of vertices or edge density you ad adjust the numVertices, numEdges parameters as it suites you. Here is an example output. Edge weights are distributed uniform randomly over [0, 1].
Here is a shortest path plot with 1500 nodes. It works but it gets difficult to visualize at this scale... You can sort of see the red vertices in there right? 🙂
You can download the Mathematica notebook for this post here.