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 nodes neighbors, generalizing these statistics from immediate one-hop neighbors to two-hop neighbors. We describe how transsortativity can be systematically varied, independently of the networks 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.
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