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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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. 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. The k-core decomposition is a widely studied summary statistic that describes a graph’s global connectivity structure. In this paper, we move beyond using k-core decomposition as a tool to summarize a graph and propose using k-core decomposition as a tool to model random graphs. We propose using the shell distribution vector, a way of summarizing the decomposition, as a sufficient statistic for a family of exponential random graph models. We study the properties and behavior of the model family, implement a Markov chain Monte Carlo algorithm for simulating graphs from the model, implement a direct sampler from the set of graphs with a given shell distribution, and explore the sampling distributions of some of the commonly used complementary statistics as good candidates for heuristic model fitting. These algorithms the provide first fundamental steps necessary for solving the following problems: parameter estimation in this ERGM, extending the model to its Bayesian relative, and developing a rigorous methodology for testing goodness of fit of the model and model selection. The methods are applied to a synthetic network as well as the well-known Sampson monks dataset. Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both unweighted and weighted scale free networks having local and global core-periphery as well as community structure. Network evolves using topological growth, self growth, and weight distribution function. To validate the correctness of proposed models, we use K-shell and S-shell decomposition methods. Simulation results show that the generated unweighted networks follow power law degree distribution with droop head and heavy tail. Similarly, generated weighted networks follow degree, strength, and edge-weight power law distributions. We further study other properties of complex networks, such as clustering coefficient, nearest neighbor degree, and strength degree correlation.