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sponds to the index of the k -shell this node belongs to. The k$_{S}$ index provides a different type of information on a node than that provided by the degree k . By definition, a given layer with index k$_{S}$ can be occupied with nodes of degree k ≥ k$_{S}$ . In the case of random model networks, such as the configurational model, there is a strong correlation between k and the k$_{S}$ index of a node and, therefore, both quantities provide the same type of informa- tion. Thus, the low-degree nodes are generally in the periphery, and the high-degree nodes are generally in the innermost k -shells. In real networks, however, this relation is often not true. In real networks hubs may have very different k$_{S}$ values and can be located both in the periphery (yellow node in Fig. 5) or in the core (blue node in Fig. 5) of the network. 

<img src='content_image/346819.jpg'>

The assignment of a k$_{S}$ index to a node is also quite robust. We have randomly removed 10% and 50% of the links in the networks that we study, simulating thus incomplete infor- 

