  Mixing patterns in large self-organizing networks, such as the Internet, the
World Wide Web, social and biological networks are often characterized by
degree-degree dependencies between neighbouring nodes. In this paper we propose
a new way of measuring degree-degree dependencies. One of the problems with the
commonly used assortativity coefficient is that in disassortative networks its
magnitude decreases with the network size. We mathematically explain this
phenomenon and validate the results on synthetic graphs and real-world network
data. As an alternative, we suggest to use rank correlation measures such as
Spearman's rho. Our experiments convincingly show that Spearman's rho produces
consistent values in graphs of different sizes but similar structure, and it is
able to reveal strong (positive or negative) dependencies in large graphs. In
particular, we discover much stronger negative degree-degree dependencies} in
Web graphs than was previously thought. {Rank correlations allow us to compare
the assortativity of networks of different sizes, which is impossible with the
assortativity coefficient due to its genuine dependence on the network size. We
conclude that rank correlations provide a suitable and informative method for
uncovering network mixing patterns.
