The impact of local processes and the prohibition of multiple links in the topological properties of directed complex networks

Abstract

Local processes exert influence on the growth and evolution of complex networks, which in turn shape the topological and dynamic properties of these networks. Some local processes have been researched, for example: Addition of nodes and links, rewiring of links between nodes, accelerated growth, link removal, aging, copying and multiple links prohibition. These processes impact directly into the topological and dynamical properties of complex networks. This paper introduces a new model for growth of directed complex networks which incorporates the prohibition of multiple links, addition of nodes and links, and rewiring of links. This paper also reports on the impact that these processes have in the topological properties of the networks generated with the proposed model. Numerical simulation shows that, when the frequency of rewiring increases in the proposed model, the γ exponent of the in-degree distribution approaches a value of 1.1. When the frequency of adding new links increases, the γ exponent approaches 1. That is the proposed model is able to generate all exponent values documented in real-world networks which range 1.05 < γ < 8.94.