Some new applications of network growth models

Abstract

The study and analysis of complex networks has in recent times sparked widespread attention from the scientific community [1, 2, 3]. This interest has been spurred partly by researchers recognizing networks as useful representations of real-world complex systems, and also due to the widespread availability of computing resources, enabling them to gather and analyze data on a scale much larger than before. Studies have ranged from large-scale empirical analysis of the World Wide Web, social networks and biological systems, to the development of theoretical models and tools to explore the various properties of these systems [4, 5]. A topic that has garnered significant interest is the subject of growing networks, inspired by real-world examples such as that of the Internet, the World Wide Web and scientific citation networks [6, 7, 8]. The particular case of the World Wide Web has led to what is perhaps the best-known body of work on this topic: the preferential attachment model [9, 10], in which vertices are added to a network with edges that attach to pre-existing vertices with probabilities depending on those vertices’ degrees. When the attachment probability is precisely linear in the degree of the target vertex, the resulting degree sequence has a power-law tail, in the limit of large network size. The appearance of the power-law tail is what first led to the popularity of growth models as a method to describe network evolution, as most real-world networks appear to have degree distributions that are approximately power laws.