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Ranking node importance is crucial in understanding network structure andfunction on complex networks. Degree, h-index and coreness are widely used, butwhich one is more proper to a network associated with a dynamical process, e.g.SIR spreading process, is still unclear. To fill this gap, a, which isextracted from the fitting function (f(x)=1-1/(e^(2a(x-b))+1)) of the averagenumber of nodes in each radius of the neighborhood of a node, is proposed.Experiment results which are carried out on twenty real-world networks showthat a can classify which of the three measures (degree, h-index and coreness)is more proper to a network in ranking node importance. We also find that [b/3]is a good indicator for forecasting the optimal radius of the neighborhood of anode in ranking node importance for a given network. To the best of ourknowledge, it is the first solution of this interesting and open issue.Furthermore, by extending the range of neighborhood where we construct anoperator H on of a node, we propose a new method to quantify the importance ofa node. The ranking accuracies of most networks can be improved when the radiusis increased from 0 to its forecasting optimal radius and the improvement, forthe best case, reaches up to 111%. The performances will reduce on half of thenetworks studied in this paper if we roughly extend the radius of theneighborhood. Our work deepens the understanding of how to find out the propernode ranking method for complex networks. The proposed methods bridge the gapsamong network structure and node importance, and may have potentialapplications in controlling the outbreak of disease, designing of optimalinformation spreading strategies.

Finding the proper node ranking method for complex networks