  While the majority of approaches to the characterization of complex networks
has relied on measurements considering only the immediate neighborhood of each
network node, valuable information about the network topological properties can
be obtained by considering further neighborhoods. The current work discusses on
how the concepts of hierarchical node degree and hierarchical clustering
coefficient (introduced in cond-mat/0408076), complemented by new hierarchical
measurements, can be used in order to obtain a powerful set of topological
features of complex networks. The interpretation of such measurements is
discussed, including an analytical study of the hierarchical node degree for
random networks, and the potential of the suggested measurements for the
characterization of complex networks is illustrated with respect to simulations
of random, scale-free and regular network models as well as real data
(airports, proteins and word associations). The enhanced characterization of
the connectivity provided by the set of hierarchical measurements also allows
the use of agglomerative clustering methods in order to obtain taxonomies of
relationships between nodes in a network, a possibility which is also
illustrated in the current article.
