reducing the variance parameter (as part of making the point that the "drop off" in the power law distribution
is not as important as the "slow decay/long tail).
Well--not exactly. Poisson distribution, as you saw, has only *one* parameter--lambda, and the
means as well as the variance of the distribution will be lambda (this is unlike normal distribution,
for example, where you can set the mean and variance parameters indepdendently). The only way to reduce
the variance is thus to reduce the mean... (you may also recall that for random networks, lambda is p*N (i.e., the expected degree))
Here is a link on poisson distribution as well as how it is the limiting case of binomial distribution: