Common neighbours and the local-community-paradigm for topological link prediction in bipartite networks

Bipartite networks are powerful descriptions of complex systems characterized by two different classes of nodes and connections allowed only across but notwithin the two classes. Unveiling physical principles, building theories and suggesting physicalmodels to predict bipartite links such as productconsumer connections in recommendation systems or drug–target interactions inmolecular networks can provide priceless information to improve e-commerce or to accelerate pharmaceutical research. The prediction of nonobserved connections starting from those already present in the topology of a network is known as the link-prediction problem. It represents an important subject both inmany-body interaction theory in physics and in new algorithms for applied tools in computer science. The rationale is that the existing connectivity structure of a network can suggest where new connections can appearwith higher likelihood in an evolving network, orwhere nonobserved connections aremissing in a partially knownnetwork. Surprisingly, current complex network theory presents a theoretical bottle-neck: a general framework for local-based link prediction directly in the bipartite domain ismissing.Here, we overcome this theoretical obstacle and present a formal definition of commonneighbour index and local-community-paradigm (LCP) for bipartite networks. As a consequence, we are able to introduce the first node-neighbourhood-based and LCP-based models for topological link prediction that utilize the bipartite domain.We performed link prediction evaluations in several networks of different size and of disparate origin, including technological, social and biological systems.Ourmodels significantly improve topological prediction inmany bipartite networks because they exploit local physical driving-forces that participate in the formation and organization ofmany real-world bipartite networks. Furthermore, we present a local-based formalism that allows to intuitively implement neighbourhood-based link prediction entirely in the bipartite domain.