In this Letter we identify the general rules that determine thesynchronization properties of interconnected networks. We study analytically,numerically and experimentally how the degree of the nodes through which twonetworks are connected influences the ability of the whole system tosynchronize. We show that connecting the high-degree (low-degree) nodes of eachnetwork turns out to be the most (least) effective strategy to achievesynchronization. We find the functional relation between synchronizability andsize for a given network-of-networks, and report the existence of the optimalconnector link weights for the different interconnection strategies. Finally,we perform an electronic experiment with two coupled star networks and concludethat the analytical results are indeed valid in the presence of noise andparameter mismatches.
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