Number of Collaborations

According to Barabasi's Emergence of scaling in random networks if one makes a similar plot for the number of connections (or ‘‘links’’) z to or from sites on the World Wide Web, the resulting distribution closely follows a power law: $P(z)\approx z^{-t}$, where t is a constant exponent with (in that case) a value of about 2.5. However, the author's data do not follow a power-law form perfectly. If they did, the curves in Fig. 2 would be straight lines on the logarithmic scales used. However, these data are well fitted by a power-law form with an exponential cutoff: $P(z)\approx z^{-t}e^{-{\frac {z}{z_{c}}}}$. where $t$ and $z_{c}$ are constants.