  Networks play a prominent role in the study of complex systems of interacting
entities in biology, sociology, and economics. Despite this diversity, we
demonstrate here that a statistical model decomposing networks into matching
and centrality components provides a comprehensive and unifying quantification
of their architecture. First we show, for a diverse set of networks, that this
decomposition provides an extremely tight fit to observed networks.
Consequently, the model allows very accurate prediction of missing links in
partially known networks. Second, when node characteristics are known, we show
how the matching-centrality decomposition can be related to this external
information. Consequently, it offers a simple and versatile tool to explore how
node characteristics explain network architecture. Finally, we demonstrate the
efficiency and flexibility of the model to forecast the links that a novel node
would create if it were to join an existing network.
