The whole frame of interconnections in complex networks hinges on a specificset of structural nodes, much smaller than the total size, which, if activated,would cause the spread of information to the whole network [1]; or, ifimmunized, would prevent the diffusion of a large scale epidemic [2,3].Localizing this optimal, i.e. minimal, set of structural nodes, calledinfluencers, is one of the most important problems in network science [4,5].Despite the vast use of heuristic strategies to identify influential spreaders[6-14], the problem remains unsolved. Here, we map the problem onto optimalpercolation in random networks to identify the minimal set of influencers,which arises by minimizing the energy of a many-body system, where the form ofthe interactions is fixed by the non-backtracking matrix [15] of the network.Big data analyses reveal that the set of optimal influencers is much smallerthan the one predicted by previous heuristic centralities. Remarkably, a largenumber of previously neglected weakly-connected nodes emerges among the optimalinfluencers. These are topologically tagged as low-degree nodes surrounded byhierarchical coronas of hubs, and are uncovered only through the optimalcollective interplay of all the influencers in the network. Eventually, thepresent theoretical framework may hold a larger degree of universality, beingapplicable to other hard optimization problems exhibiting a continuoustransition from a known phase [16].
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