Finding important nodes via improved cycle ratio method

The cycle ratio method is designed to define the importance of nodes by the cycles of a network, and a set of important nodes identified by this method has superior control performance than by degree centrality, H-index, and coreness methods in several aspects such as spreading, percolation, and pinning control. Unfortunately, the method is not precise enough to portray the importance of the nodes, so in this paper, we improve the cycle ratio method by reducing the impact of four and larger cycles and adding the effects of the tree structure. Through numerical simulations on several real networks, we find that the set of important nodes discovered by the improved cycle ratio method is more dispersed and has better control in all three aspects of spreading, percolation, and pinning control than the original cycle ratio method. The work in this paper makes it more accurate to use the cycle structure to find a set of important nodes in a network and provides new ideas for a deeper understanding of the effects of local structure on the importance of the nodes.