Matching-centrality decomposition and the forecasting of new links in networks

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. The matching term quantifies the assortative structure in which node makes links with which other node, while the centrality term quantifies the number of links that nodes make. We show, for a diverse set of networks, that this decomposition can provide a tight fit to observed networks. Then we provide three applications. First, we show that the model allows very accurate prediction of missing links in partially known networks. Second, when node characteris- tics 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 ex- plai...