Fig. 3: Visualization of the rankings of nodes produced by degree, H-index, coreness, and cycle ratio.

The Yeast network is taken for example. In each plot, the sizes and colors of nodes are proportional to their relative values of the corresponding indices normalized by their respective maximum values. The position of each node in the four plots is fixed. For example, in (a), a node i’s relative value is \(k_i/k_{{{\mathrm{max}}}}\) where \(k_i\) is i’s degree and \(k_{{{\mathrm{max}}}}\) is the maximum degree of Yeast. Analogously, (b–d) show the results of H-index, coreness and cycle ratio, respectively. In (a–c), the vital nodes are densely connected with each other and clustered in several certain regions, and this effect increases in turn. In (d), however, the situation is completely different where the vital nodes scattered throughout the whole network.