  Assortativity, i.e. the tendency of a vertex to bond with another based on
their similarity, such as degree, is an important network characteristic that
is well-known to be relevant for the network's robustness against attacks.
Commonly it is analyzed on the global level, i.e. for the whole network.
However, the local structure of assortativity is also of interest as it allows
to assess which of the network's vertices and edges are the most endangering or
the most protective ones. Hence, it is quite important to analyze the
contribution of individual vertices and edges to the network's global
assortativity. For unweighted networks M. Piraveenan, M. Prokopenko, and A. Y.
Zomaya (2008, 2010) and Guo-Qing Zhang, Su-Qi Cheng, and Guo- Qiang Zhang
(2012) suggest two allegedly different approaches to measure local
assortativity. In this paper we show their equivalence and propose generalized
local assortativity measures that are also applicable to weighted (un)directed
networks. They allow to analyze the assortative behavior of edges and vertices
as well as of entire network components. We illustrate the usefulness of our
measures based on theoretical and real-world weighted networks and propose new
local assortativity profiles, which provide, inter alia, information about the
pattern of local assortativity with respect to edge weight.
