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We define a new concept, a hyperstructure, which is related to networks and hypernetworks and allows us to represent real problems. We also define the efficiency of this hyperstructure and we apply it to an example. [ABSTRACT FROM AUTHOR]

It is important to know how to improve a network when dealing with performance and security. We characterize the optimal design of a network for efficiency or vulnerability giving the extreme networks for those parameters. Moreover, we give an algorithm to improve the vulnerability of a given network when adding a new link. For efficiency, we present two facts that have to be considered in order to improve it when adding a new link, and we calculate bounds for the increment. [ABSTRACT FROM AUTHOR]