Generalized entropies and open random and scale-free networks

We propose the concept of open network as an arbitrary selection of nodes of a large unknown network. Using the hypothesis that information of the whole network structure can be extrapolated from an arbitrary set of its nodes, we use Rényi mutual entropies in different qorders to establish the minimum critical size of a random set of nodes that represents reliably the information of the main network structure. We also identify the clusters of nodes responsible for the structure of their containing network.