Understanding Complex Network Models

Abstract The interest in networks has started with the concept of graph theory in the mathematical literature, where the term graph was used instead of network. In the context of network theory, complex network comprises points of connections or nodes and the interactions or links between them tying the nodes. In the past centuries, graph theory has been focused on regular graph? without apparent design ideologies for describing random graphs? which was introduced as the simplest realization of complex networks. Owing to advances in computing power and large databases on the topologies of real world networks, many new concepts and measures were then prompted. Along this route, various models have been developed to describe small world phenomenon and scale free structure of many real world networks. While there has been a growing popular literature attesting the source of datasets for such network models, researchers from different disciplines appear motivated to adopt tools relevant to their domain. This paper introduces two different programs written in Java for generating prototypes of datasets for the main network models covering regular, random, small-world and scale free networks.When used precisely, they produce accurate and comprehensive datasets of the models. Therefore, the proposed programs provideideal tools for understanding and predicting the behavior of real world complex networks. Additionally, the paper presents theoretical concepts of the models and further illustrates some mathematical derivations to support the concepts.