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.
Initially, the k-shell decomposition method was defined for undirected unweighted networks, but recently it has been extended to different types of networks. extended the k-shell method to identify the core-periphery structure in weighted networks @cite_67 . They defined the weighted degree that considers both the degree as well as the weights of the connected edges. Then, the weighted degree is used while applying the k-shell decomposition method. also proposed a method to identify the core-periphery structure in weighted networks where they only consider the strength of the nodes while pruning the nodes in each iteration @cite_17 . This method is known as s-shell decomposition method or strength decomposition method. proposed an edge-weighting k-shell method where they consider both the degree as well as the edge-weights, and the edge weight is computed by adding the degree of its two endpoints @cite_36 . The importance of both of these parameters can be set using a tuning parameter which varies from 0 to 1.
@cite_36 @cite_67 @cite_17
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Identifying influential nodes in complex networks has attracted much attention because of its great theoretical significance and wide application. Existing methods consider the edges equally when designing identifying methods for the unweighted networks. In this paper, we propose an edge weighting method based on adding the degree of its two end nodes and for the constructed weighted networks, we propose a weighted k-shell decomposition method (Wks). Further investigations on the epidemic spreading process of the Susceptible–Infected–Recovered (SIR) model and Susceptible–Infected (SI) model in real complex networks verify that our method is effective for detecting the node influence. We present a generalized method for calculating the k-shell structure of weighted networks. The method takes into account both the weight and the degree of a network, in such a way that in the absence of weights we resume the shell structure obtained by the classic k-shell decomposition. In the presence of weights, we show that the method is able to partition the network in a more refined way, without the need of any arbitrary threshold on the weight values. Furthermore, by simulating spreading processes using the susceptible- infectious-recovered model in four different weighted real-world networks, we show that the weighted k-shell decomposition method ranks the nodes more accurately, by placing nodes with higher spreading potential into shells closer to the core. In addition, we demonstrate our new method on a real economic network and show that the core calculated using the weighted k-shell method is more meaningful from an economic perspective when compared with the unweighted one.