Random graphs simulation

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Reading the article "Emergence of scaling in random network, by Barabasi and Albert"

I faced a lot of results obtained by simulations of the A-B random graph model. I always wanted to do such simulations, but honestly I don't know how to start. There is a better programming language? There are packages? There is a special software to handle heavy data?

To put everything in one question: how they do that kind of simulation?