  A network's assortativity is the tendency of vertices to bond with others
based on similarities, usually excess vertex degree. In this paper we consider
assortativity in weighted networks, both directed and undirected. To this end,
we propose to consider excess vertex strength, rather than excess degree, and
show, that assortativity in weighted networks can be broken down into two
mechanisms, which we refer to as the connection effect and the amplification
effect. To capture these effects we introduce a generalised assortativity
coefficient. This new coefficient allows for a more detailed interpretation and
assessment of assortativity in weighted networks. Furthermore, we propose a
procedure to assess the statistical significance of assortativity using
jackknife, bootstrap and rewiring techniques. The usefulness of our proposed
generalised assortativity coefficient is demonstrated by an in-depth analysis
of the assortativity structure of several weighted real-world networks.
