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On Wednesday 19 November 2003 05:06 am, David Lusseau wrote:
>
> The fact that the random networks are composed of many isolates is an
> interesting fact in itself. If re-iterated many times, one could get the
> likelihood that, given the number of nodes and links observed in the
> real-world network, all nodes are connected in one giant cluster. If it is
> unlikely (observed once or twice over 100-1000 re-iterations or whatever
> level of significance one wants to choose) this tells us a lot about the
> real-world network: it is most likely not based on a random attachment
> mechanism.


Or one can calculate such things exactly (to order 1/n, where n is the
graph size).  Formulas for such things can be found in this paper:

  http://arxiv.org/abs/cond-mat/0007235/

Mark Newman

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