A Model for Scale-Free Networks: Application to Twitter

In the last few years, complex networks have become an increasingly relevant research topic due to the large number of fields of application. Particularly, complex networks are especially significant in the area of modern online social networks (OSNs). OSNs are actually a challenge for complex network analysis, as they present some characteristics that hinder topology processing. Concretely, social networks' volume is exceedingly big, as they have a high number of nodes and links. One of the most popular and influential OSNs is Twitter. In this paper, we present a model to describe the growth of scale-free networks. This model is applied to Twitter after checking that it can be considered a scale-free complex network fulfilling the small world property. Checking this property involves the calculation of the shortest path between any two nodes of the network. Given the difficulty of this computation for large networks, a new heuristic method is also proposed to find the upper bounds of the path lengths instead of computing the exact length.