As can be shown again by approximating sum by integral, all the moments $\langle k^m \rangle$of a power law distribution diverge for $m>\alpha-1$. Of course, this is in the limit of an infinite system with the same distribution, in finite systems (as in networks with a finite number of nodes), the moment will of course be finite (for a network, $k$ will have a maximum value, cutting off the domain of the integral used to calculate $C$).