Rational graph: a model for complex networks

Real life networks like social, biological and technical networks have amazing characteristics. These networks grow rapidly by the continuous addition of new nodes without following any organisation. Despite their huge sizes, these networks have a short path length, high clustering and power law degree distribution. Here, we investigate the topological characteristics of these types of networks. We also explore the main graph models that have been proposed to represent the dynamics and growth of these networks. This work provides an original contribution to build a complex network model. Motivated by the structural characteristics of complex networks and the deficiencies in the existing graph models, we are proposing the rational model, which is a model that imitates the characteristics of complex networks. The model was implemented and examined against other complex network models. The results showed that the rational model imitates the growth behaviour of the network, while maintaining the expected topological properties of the network.