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Well, usually (see Pastor-Satorras & Vespignani (2004). Evolution &
Structure of the Internet. Cambridge: Cambridge University Press), the
formula $<l> \sim \logN / \log<k>$ is attributed to B. Bollobas
(1981) and Bollobas & de la Vega (1982) - I can send you the detailed
references if you wish.

To be more accurate, Bollobas has considered the diameter of a random
k-regular graph and showed that $\diam(G_{N,k-reg} \sim \logN / \log(k-1)$
and $\diam(G_{N,k-reg} \sim <l>$, "with high probability" asymptotically
for $N$.

I'm afraid this does not answer your question. In any case, you have to
check out the detailed algorithms used in the numerical computations of these
quantities, which are implemented in the software packages you're using.

--Moses Boudourides

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