In a Barabasi-Albert model, which is a special kind of scale-free graphs, the degree distribution of each node is
$$P(k) \sim k^{-3}$$
Given $\| V \|$ (number of nodes), how can I compute "number of nodes whose degree distribution is less than or equal to $k$ (cumulative distribution)"?
Note that the concern here is "~"! I am not sure, but I think in order to compute the degree distribution and its cumulative, I should turn "$\sim$" into "=" (How?)
Of course I can generate some graphs and make use of sampling to estimate the exact degree distribution, but is there a way to mathematically estimate it?