  Uncovering the hidden regularities and organizational principles of networks
arising in physical systems ranging from the molecular level to the scale of
large communication infrastructures is the key issue for the understanding of
their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon
refers to the tendency of nodes with high centrality, the dominant elements of
the system, to form tightly interconnected communities and it is one of the
crucial properties accounting for the formation of dominant communities in both
computer and social sciences [4-8]. Here we provide the analytical expression
and the correct null models which allow for a quantitative discussion of the
rich-club phenomenon. The presented analysis enables the measurement of the
rich-club ordering and its relation with the function and dynamics of networks
in examples drawn from the biological, social and technological domains.
