  We study assortative mixing in networks, the tendency for vertices in
networks to be connected to other vertices that are like (or unlike) them in
some way. We consider mixing according to discrete characteristics such as
language or race in social networks and scalar characteristics such as age. As
a special example of the latter we consider mixing according to vertex degree,
i.e., according to the number of connections vertices have to other vertices:
do gregarious people tend to associate with other gregarious people? We propose
a number of measures of assortative mixing appropriate to the various mixing
types, and apply them to a variety of real-world networks, showing that
assortative mixing is a pervasive phenomenon found in many networks. We also
propose several models of assortatively mixed networks, both analytic ones
based on generating function methods, and numerical ones based on Monte Carlo
graph generation techniques. We use these models to probe the properties of
networks as their level of assortativity is varied. In the particular case of
mixing by degree, we find strong variation with assortativity in the
connectivity of the network and in the resilience of the network to the removal
of vertices.
