Resumen de Influence maximization in complex networks through optimal percolation
Flaviano Morone, Hernán A. Makse
The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network1, or, if immunized, would prevent the diffusion of a large scale epidemic2,3. Localizing this optimal, that is, minimal, set of structural nodes, called influencers, is one of the most important problems in network science4,5. Despite the vast use of heuristic strategies to identify influential spreaders6-14, the problem remains unsolved. Here we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix15 of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. The present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase16.
