For Gnutella, we know as the standard TTL8 and the number of nodes computed by the Gnutella crawler. Using the formula, we compute the dimension and the average number of outgoing connections .
Milgram's experiment showed that in the United States, a country with about 250 million () inhabitants, there are 6 () degrees of separation. The formula estimates that each person knows about 25 people enough well to perform the experiment.
Using Milgram's , we compute for the entire world, for Switzerland and for a little village in the mountains.
We try the formula on the brain, a complex network with 100 billion neurons. Each neuron has about 15000 connections but is connected to a neighborhood of about 10 other neurons only, about 1500 connections for each neuron. The path length would be then 218. We idealized the CPU as it would be composed by 3 million NAND ports, with 2 inputs and one output.
However, Gnutella and the above mentioned problems are far from homogeneous in the degree of the nodes, so that our formula gives only a rough estimation.