The Accuracy of Power Law Based Similarity Model in Phonebook-Centric Social Networks

Social networks are becoming increasingly popular nowadays. The increasing capabilities of mobile phones enable them to participate in such networks. We should consider the fact, that the phonebooks in the mobile devices represent social relationships that can be integrated in the social networks. Such networks provide a synchronization mechanism between phonebooks of the users and the social network which allows detecting other users listed in the phonebooks. Users can accept detected similarities. After that, if one of their contacts changes her or his personal detail, it will be propagated automatically into the phonebooks, after considering privacy settings. Estimating the total number of these similarities is a key issue from scalability point of view in such networks. We implemented a phonebook-centric social network, called Phonebookmark and investigated the structure of the network. Previously it was shown that the distribution of similarities follows a power law. Also a model was proposed by us, which can be used to calculate the total number of similarities. However the accuracy of the model is another question, because of the infinite variance of the power law distribution. The contribution of this paper is that using the fact that a member of the network can only be involved in a limited number of similarities results in a similarity distribution with a finite variance. Therefore, central limit theorems can be used to show the accuracy of our estimation of the total number of similarities. However the model can be used in other power law distributions which apply to the requirements.