Evaluate Node Importance by Decomposing Network With a Recursive Percolation Process

Due to structural heterogeneity, the main function and structure of networked systems are significantly influenced by some important nodes rather than each member. In practical, the properties of important nodes could be different from network to network, and thus a variety of algorithms have been specially designed to identify important nodes of different networks and of different dynamics. In this paper we propose a widely applicable algorithm by employing the percolation model in statistical physics, which describes the behavior of connected clusters when nodes are connected randomly. This algorithm appropriately combines the local and global properties of a network, thus it stresses the significance of nodes that neither have a visibly local importance, such as degree and clustering, nor have a visibly global importance, such as betweenness. The effectiveness of our algorithm has been illustrated in a series of networks, including model networks with different degree distributions and different degree correlations, and empirical networks. As a shell decomposition process, the framework of our algorithm has extensive application prospects in analyzing network structure, such as community, core–periphery structure, and shell structures.