An empirical relation between k-shells and the h-index in scale-free networks

After clarifying the definitions of h-index and k-shells in a graph, it is shown that the largest k value for which there exists a non-empty k-shell, denoted as kmax(G), satisfies the relation kmax(G) ? h(G) , where h(G) is the degree h-index of graph G. Next we determine an empirical relation between the hindex, the number of nodes in a small scale-free network, i.e. with maximum degree centrality < 100, and the coreness and degree centrality of its nodes. In this contribution we embed the information sciences among other fields involved in network studies.