Several models have been proposed that describe the evolution of the graph properties of many online social networks (OSNs) and explain the behavior of their users. These models are essential for understanding the growth dynamics of the underlying social graph. One of the most prominent OSNs is Twitter, since it covers a significant part of the online worldwide population. Nevertheless, investigating the validity of these models on Twitter entails many difficulties. The size of Twitter and the limitations of its access API make extremely difficult the estimation of many graph properties and therefore the evaluation of the proposed models. In this study, we present a simple and efficient method to fit an already existing model, which describes the densification power law property of modern OSNs. This model states that the average degree of an OSN increases over time. In a case study, we assess this model in two large samples of Twitter, and we demonstrate how it can portray the altering growth periods of Twitter. Finally, we make some remarks on several events during the early period of Twitter that may have affected its growth rates.
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