  Rich-club, assortativity and clustering coefficients are frequently-used
measures to estimate topological properties of complex networks. Here we find
that the connectivity among a very small portion of the richest nodes can
dominate the assortativity and clustering coefficients of a large network,
which reveals that the rich-club connectivity is leveraged throughout the
network. Our study suggests that more attention should be payed to the
organization pattern of rich nodes, for the structure of a complex system as a
whole is determined by the associations between the most influential
individuals. Moreover, by manipulating the connectivity pattern in a very small
rich-club, it is sufficient to produce a network with desired assortativity or
transitivity. Conversely, our findings offer a simple explanation for the
observed assortativity and transitivity in many real world networks --- such
biases can be explained by the connectivities among the richest nodes.
