How to generate random graphs?

Question

I want to be able to generate random, undirected, and connected graphs in Java. In addition, I want to be able to control the maximum number of vertices in the graph. I am n

Answer 1

The only tricky part is ensuring that the final graph is connected. To do that, you can use a disjoint set data structure. Keep track of the number of components, initially n. Repeatedly pick pairs of random vertices u and v, adding the edge (u, v) to the graph and to the disjoint set structure, and decrementing the component count when the that structure tells you u and v belonged to different components. Stop when the component count reaches 1. (Note that using an adjacency matrix simplifies managing the case where the edge (u, v) is already present in the graph: in this case, adj[u][v] will be set to 1 a second time, which as desired has no effect.)

If you find this creates graphs that are too dense (or too sparse), then you can use another random number to add edges only k% of the time when the endpoints are already part of the same component (or when they are part of different components), for some k.