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| Competition between systems that belong to a complex network relies on several dynamical and topological aspects such as their natural frequencies (or time scales), number of neighbors or location inside the network. Nevertheless, the fact that real networks are usually embedded in networks of networks (NoN) also has important consequences in competition processes. In the current contribution, we present a new framework to analyze the competition between interconnected networks for available resources as a struggle for network importance, measured via the eigenvector centrality. Our analytical and numerical results yield that different strategies must be played depending on the initial network structures. In particular, competitor networks can strikingly improve their outcome by selecting the adequate connector nodes or by rearranging their internal topology. Due to the existence of optimal strategies, we are able to define a competition parameter $\Omega$ that quantifies the benefit of the interconnection topology in real networks. These results can be applied to a large number of biological processes in networks related with evolutionary, spreading or diffusion processes. |
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