Towards finding the best-fit distribution for OSN data

Currently, all online social networks (OSNs) are considered to follow a power-law distribution. In this paper, the degree distribution for multiple OSNs has been studied. It is seen that the degree distributions of OSNs differ moderately from a power law. Lognormal distributions are an alternative to power-law distributions and have been used as best fit for many complex networks. It is seen that the degree distributions of OSNs differ massively from a lognormal distribution. Thus, for a better fit, a composite distribution combining power-law and lognormal distribution is suggested. This paper proposes an approach to find the most suitable distribution for a given degree distribution out of the six possible combinations of power law and lognormal, namely power law, lognormal, power law-lognormal, lognormal-power law, double power law, and double power law lognormal. The errors in the fitted composite distribution and the original degree distribution of the OSNs are observed. It is seen that a composite distribution fitted using the approach described in this paper is always a better fit than both power-law and lognormal distributions.