FORMAL ANALYSIS OF WEIGHTED LONGITUDINAL ROUTERS NETWORK VIA SCALE-FREE NETWORK. A CASE STUDY

The process of identifying the central nodes in complex networks research has remained interesting and very important issue for network analysis. The identification of main nodes in the network can lead to many answers for the solution of security and other problems depending on the type of complex networks under analysis. Different topological metrics of the network can be used to locate the major nodes in the network but the degree and betweenness (Load) centralities perform very important role in evolution and communication of nodes in growing networks. Unfortunately, these metrics have been analyzed in different complex systems mainly either on the bases of the number of links to nodes in the network or with much focused from the perspective of weights of links. Therefore, locating the main nodes in the network not only depends on links but majorly on weight of links. Routers network of the internet is an example of scale-free nature which follow power-law distribution and causes inhomogeneous structure with some nodes with large number of links while many with a few. Further, in this type of distribution few nodes become very important. In this paper, we analyze the behavior of routers network by using two metrics of centralities with weighted and un-weighted links based on the dataset of PTCL routers network in Pakistan. Furthermore, by using centralities measures we try to show that weight of links is important as compare to number of links by following the concept from “rich get richer” to “fit get richer” in routers network. Moreover, we prove that weighted routers network is very close to scale-free networks as compared to unweighted, and due to this phenomenon these networks sustain their robustness.