生成大型无向加权图

Question

A random large connected undirected graph in JAVA with 5K vertices and D density is to be generated. But generating an edge between random V1 and a random V2 is taking a lot of time. I tried eliminating a created edge from the list of all possible edges and then selecting a random one from the remaining edges, but again it is taking a lot of time.

What do you think will be a fast way to generate the edges for the huge connected graph in a random fashion?

Answer 1

You have N = 5k number of vertixes. You need M = number of edges. Its fixed or random? If random it's a number between 1 and N*N. Just create a random number from randomizer.

Then in a look generate M pairs of random numbers each 0<=P1 and P2<=N. Each pair is an edge. Then just add weight to the pair.

Answer 2

The easiest solution i can think of (might be cheating), would be to loop through each vertex and create an edge from itself to the next vertex in the list. This would meet the criteria of it being connected, then you could generate random edges until you meet the required density by generating a random number between 0 and the length of the list of vertices for the start and end of the edge and creating it.