Calculus and its applications in scale-free networks

Abstract

The purpose of this article is to highlight and emphasize the applications of calculus in scale-free networks, which have been found as property of many complex networks. There are many different types of real and manmade complex networks in various domain of life ranging from technological, social, biological, transportation and ecological networks among many others. All these networks have shown many similar structural properties in their formation and functions. This article focuses on the most prevalence type of networks known as Scale-Free Networks (SFN). These types of networks have two basic properties: growth and preferential node attachment. In this paper, we analyze and discuss the importance and usage of calculus in understanding the formation of these type of networks, as these networks continuously change their topology by inclusion of new nodes and links as they evolve. Further, as the calculus is the mathematical study of change therefore the applications of calculus in evolution process of complex networks with fitness model have been explained analytically based on fit-get-rich phenomenon in the complex networks as compared to simple BA1 model which is based, only on the consideration of number of nodes linkages in the networks.