Given a set of vertices, how do you create a strongly connected directed graph with an almost minimal number of edges?

Question

I am trying to test on my graph class dijkstras algorithm. To do this, I create a graph with several thousand vertices, and then create a graph connected by randomly adding thousands of edges until the graph is connected. Then I can search between any two random vertices again and again and make sure there is a path between them. The problem is that I often end up with an almost dense graph, which, since I use the adjacency list view, causes my search algorithm to be very slow.

Question : Given the set of vertices V, how do you create a strongly connected oriented graph that has significantly fewer edges than a dense graph over the same vertices?

I thought just to do the following:

vertex 1 <--> vertex 2, vertex 2 <--> vertex 3, ..., vertex n-1 <--> vertex n

And then randomly adding as n / 10 edges across the graph, but this doesn't seem like the best way to pick random graph structures to test my search algorithms.

Answer 1

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