Read section 4
We present several arguments suggesting n log(n). The one that you want is in section 4.
Zipf's law says that the value of the n'th thing tends to be 1/n times the value of the first. This has been found to apply in a wide range of different areas. (Personal wealth, size of cities, etc.) If this holds for the potential value of connections over networks, and the value of the most important connections is fixed by the medium and human nature, then the average value from being in a network is the value of the most valuable times (1 + 1/2 + ... + 1/n) which scales as log(n). Over n people this totals n log(n).
Cheers,
Ben
