The impact of node arrival process and stochastic edge growth on scale-free distribution in complex networks

Abstract

ABSTRACT A variety of proposals has been introduced to dynamically complete scale-free (SF) networks that are utilized to generate Barabási-Albert (BA) graph models. The analytical method for analysis of real networks, which is based on uniform distributions proposed in the BA model, does not seem so perfect. Consequently, some scholars refined and extended the BA model among which non-linear preferential attachment (NLPA), dynamical edge rewiring, fitness models and other growth models presented in the literature. In a network, features like how individuals enter the network, the probability distribution of edge growth, and the probability distribution of nodes’ age have considerable significance. A key question that neglects in the BA model is that ‘Can LPA phenomenon basically generate SF graphs apart from the arrival process of nodes and the probability distribution of nodes’ age?’. In this paper, we demonstrate the resulted graphs belong to the class of small-world or random networks contrary to the employ of LPA in the proposed model. Hence, what neglect in the BA model prevents us from attaining a clear interpretation of all properties of real-world networks. This study attempts to uncover these features by proposing an extended BA model.