  Network topologies can be non-trivial, due to the complex underlying
behaviors that form them. While past research has shown that some processes on
networks may be characterized by low-order statistics describing nodes and
their neighbors, such as degree assortativity, these quantities fail to capture
important sources of variation in network structure. We introduce a property
called transsortativity that describes correlations among a node's neighbors,
generalizing these statistics from immediate one-hop neighbors to two-hop
neighbors. We describe how transsortativity can be systematically varied,
independently of the network's degree distribution and assortativity. Moreover,
we show that it can significantly impact the spread of contagions as well as
the perceptions of neighbors, known as the majority illusion. Our work improves
our ability to create and analyze more realistic models of complex networks.
