On the Value of a Social Network

Different laws have been proposed for the value of a social network. According to Metcalfe’s law, the value of a network is proportional to n where n is number of users of the network, whereas Odlyzko et al propose on heuristic grounds that the value is proportional to n log n, which is the Zipf’s law. In this paper we have examined scale free, small world and random social networks to determine their value. We have found that the Zipf’s law describes the value for scale free and small world networks although for small world networks the proportionality constant is a function of the probability of rewiring. We have estimated the function associated with different values of rewiring to be described well by a quadratic equation. We have also shown experimentally that the value of random networks lies between Zipf’s law and Metcalfe’s law.