FIG. 12: k -shell structure of the analyzed networks. ( Top row ): Visualization of the k -shell structure. We represent networks as sets of concentric circles of nodes, each one corresponding to the particular k -shell, with low k$_{S}$ values in the periphery and large k$_{S}$ values towards the center of the network. The size of each visualized node is proportional to the logarithm of its degree value. We highlight the 25 highest degree nodes with black squares. Many of the hubs are found in outer layers. ( Bottom row ): Scatter plots of node degree k as a function of its k -shell index k$_{S}$ for the original networks (black symbols) and the degree-preserving randomized version of the networks (red symbols). The networks correspond to: the cond-mat collaboration network, the actor network, the email contact network, the RL Internet, the AS Internet, and the Product 11