Information flow, opinion, and epidemics spread over structured networks. When using individual node centrality indicators to predict which nodes will be among the top influencers or spreaders in a large network, no single centrality has consistently good predictive power across a set of 60 finite, diverse, static real-world topologies from six categories of social networks. We show that multi-centrality statistical classifiers, trained on a sample of the nodes from each network, are instead consistently predictive across diverse network cases. Certain pairs of centralities cooperate particularly well in statistically drawing the class boundary between the top spreaders and the rest: local centralities measuring the size of a node's neighbourhood combine well with global centralities such as the eigenvector centrality, closeness, or the core number. As a result, training classifiers with seven classical centralities leads to a nearly maximum average precision function (0.995).