Power Laws

I am not sure how much can be said about this paper. It's not that the paper is short on material, it's just that I can't think of any way to summarize it other than stating the laws that they have discovered.

The basic idea of this paper is that various properties of the internet follow power laws. That is, variables are proportional to other variables raised to constant powers. These constants may vary a little over time, or, as in the case of the eigenvalues, may be true constants.

Here are the results:

• The outdegree of a node is proportional to its "rank" (its rank according to its degree) raised to the power R, which ranged from -0.82 to -0.74 .
• The frequency of a given degree is proportional to the degree raised to the outdegree power, which seems to be a constant between -2.2 and -2.15 .
• The number of neighbors of a node that are within h hops is proportional to h to a power H.
• The eigen value lambda_i (where they are sorted in order) is proportional to i ^(-0.5), regardless of era.

With the exception of the outdegree, these power seem to be constants regardless of the growth of the internet.