Self-similarity in complex networks

Abstract

Complex networks have been studied and modeled extensively due to their relevance in various real-world systems such as the world-wide-web, telecommunication network and a variety of social networks. A large number of real-world networks are called ”scale-free” because they show a power-law distribution in the number of edges per node. Further, until recently it was widely believed that complex networks are not invariant or self-similar. This conclusion originates from the ‘small-world’ property of these networks, which implies that the number of nodes increases exponentially with the ‘diameter’ of the network rather than the power-law relation expected for a self-similar structure. In a recent paper [5], it was shown that real-world networks do indeed show self similarity under spacial scaling. They utilized the concept of boxing algorithms to introduce the concept of scale in networks. Our work aims to build further on this by showing that this property holds for various different types of social networks. Further, we also extend the spacial concept to other dimensions like temporal and semantic dimensions.