For network scientists, it has always been an interesting problem to identify the influential nodes in a given network. The k-shell decomposition method is a widely used method which assigns a shell-index value to each node based on its influential power. The k-shell method requires the global information of the network to compute the shell-index of a node that is infeasible for large-scale real-world dynamic networks. In this work, we propose a method to estimate the shell-index of a node using its local information. We also propose hill-climbing based approach to hit the top-ranked nodes in a small number of steps. We further discuss a method to estimate the rank of a node based on the proposed estimator.
In recent years there has been a growing interest in the role of networks and clusters in the global economy. Despite being a popular research topic in economics, sociology and urban studies, geographical clustering of human activity has often been studied by means of predetermined geographical units, such as administrative divisions and metropolitan areas. This approach is intrinsically time invariant and it does not allow one to differentiate between different activities. Our goal in this paper is to present a new methodology for identifying clusters, that can be applied to different empirical settings. We use a graph approach based on k-shell decomposition to analyze world biomedical research clusters based on PubMed scientific publications. We identify research institutions and locate their activities in geographical clusters. Leading areas of scientific production and their top performing research institutions are consistently identified at different geographic scales.