  A widely recognized organizing principle of networks is structural homophily,
which suggests that people with more common neighbors are more likely to
connect with each other. However, what influence the diverse structures
embedded in common neighbors have on link formation is much less
well-understood. To explore this problem, we begin by characterizing the
structural diversity of common neighborhoods. Using a collection of 120
large-scale networks, we demonstrate that the impact of the common neighborhood
diversity on link existence can vary substantially across networks. We find
that its positive effect on Facebook and negative effect on LinkedIn suggest
different underlying networking needs in these networks. We also discover
striking cases where diversity violates the principle of homophily---that is,
where fewer mutual connections may lead to a higher tendency to link with each
other. We then leverage structural diversity to develop a common neighborhood
signature (CNS), which we apply to a large set of networks to uncover unique
network superfamilies not discoverable by conventional methods. Our findings
shed light on the pursuit to understand the ways in which network structures
are organized and formed, pointing to potential advancement in designing graph
generation models and recommender systems.
