What platform is best for simulating a stochastic process on a graph/network?

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I'm simulating a dynamic process which was so far done only on a lattice, and Matlab was quite sufficient for that.

However, I can't seem to find a convenient way to model such a process on a graph such that there is clear visualisation of the process, and also return and storage of some relevant data at each stage.

Thank you.

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Have you tried using $R$? For instance see http://statisticalrecipes.blogspot.com/2013/01/easy-introduction-to-markov-chains-in-r.html

For visualization see here for example.

By the way, this visualization looks really nice, but runs in Javascript, not R.