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Topological link-prediction can exploit the entire network topology (globalmethods) or only the neighbourhood (local methods) of the link to predict.Global methods are believed the best. Is this common belief well-founded?Stochastic-Block-Model (SBM) is a global method believed as one of the bestlink-predictors, therefore it is considered a reference for comparison. But,our results suggest that SBM, whose computational time is high, cannot ingeneral overcome the Cannistraci-Hebb (CH) network automaton model that is asimple local-learning-rule of topological self-organization proved as thecurrent best local-based and parameter-free deterministic rule forlink-prediction. To elucidate the reasons of this unexpected result, weformally introduce the notion of local-ring network automata models and theirrelation with the nature of common-neighbours' definition in complex networktheory. After extensive tests, we recommend Structural-Perturbation-Method(SPM) as the new best global method baseline. However, even SPM overall doesnot outperform CH and in several evaluation frameworks we astonishingly foundthe opposite. In particular, CH was the best predictor for synthetic networksgenerated by the Popularity-Similarity-Optimization (PSO) model, and itsperformance in PSO networks with community structure was even better than usingthe original internode-hyperbolic-distance as link-predictor. Interestingly,when tested on non-hyperbolic synthetic networks the performance of CHsignificantly dropped down indicating that this rule of networkself-organization could be strongly associated to the rise of hyperbolicgeometry in complex networks. The superiority of global methods seems a"misleading belief" caused by a latent geometry bias of the few small networksused as benchmark in previous studies. We propose to found a latent geometrytheory of link-prediction in complex networks.

Local-ring network automata and the impact of hyperbolic geometry in complex network link-prediction