Key node recognition in complex networks based on the K-shell method

Key node recognition methods for complex networks often have insufficient resolution and accuracy. This study developed a K-shell based key node recognition method for complex networks that first stratifies the network to obtain the K-shell (K_s) values for each node that indicate the influence of the global structure of the complex network. A comprehensive degree (CD) was then defined that balances the various influences of neighboring nodes and sub-neighboring nodes. A dynamic adjustable influence coefficient, μ_i, was also defined. Nodes with the same K_s but larger comprehensive degrees are more important. Tests show that this method more effectively identifies key nodes than several classical key node recognition methods and a risk assessment method, and has high accuracy and resolution in different complex networks. This method provides network node risk assessments that can be used to protect important nodes and to determine the risk disposal priority of the network nodes.