Network Evolution: Theory and Mechanisms

Abstract

In this chapter, we intend to give a review on some of the important network models that are introduced in recent years. The aim of all of these models is to imitate the real-world network properties. Real-world networks exhibit be- haviors such as small-world, scale-free, and high clustering coefficient. One of the significantmodels known as Barab´ asi–Albertmodel utilizes preferential attachment mechanism as a main mechanism for power-law networks generation. Ubiquity of preferential attachment in network evolution has been proved for many kinds of networks. Additionally, one can generalize functional form of the preferential attachment mathematically, where it provides three different regimes. Besides, in real-world networks, there exist natural constraints such as age or cost that one can consider; however, all of these models are classified as global models. Another im- portant family of models that rely on local strategies attempt to realize network evolution mechanism. These models generate power-law network through making decisions based on the local properties of the networks.