  Large scale hierarchies characterize complex networks in different domains.
Elements at their top, usually the most central or influential, may show
multipolarization or tend to club forming tightly interconnected communities.
The rich-club phenomenon quantified this tendency based on unweighted network
representations. Here, we define this metric for weighted networks and discuss
the appropriate normalization which preserves nodes' strengths and discounts
structural strength-strength correlations if present. We find that in some real
networks the results given by the weighted rich-club coefficient can be in
sharp contrast to the ones in the unweighted approach. We also discuss that the
scanning of the weighted subgraphs formed by the high-strength hubs is able to
unveil features contrary to the average: the formation of local alliances in
rich-multipolarized environments, or a lack of cohesion even in the presence of
rich-club ordering. Beyond structure, this analysis matters for understanding
correctly functionalities and dynamical processes relying on hub
interconnectedness.
