  In many networks, including networks of protein-protein interactions,
interdisciplinary collaboration networks, and semantic networks, connections
are established between nodes with complementary rather than similar
properties. While complementarity is abundant in networks, we lack mathematical
intuition and quantitative methods to study complementarity mechanisms in these
systems. In this work, we close this gap by providing a rigorous definition of
complementarity and developing geometric complementarity frameworks for
modeling and inference tasks on networks. We demonstrate the utility of
complementarity frameworks by learning geometric representations of several
real systems. Complementarity not only offers novel practical analysis methods
but also enhances our intuition about formation mechanisms in networks on a
broader scale and calls for a careful re-evaluation of existing
similarity-inspired methods.
