  Bipartite networks are powerful descriptions of complex systems characterized
by two different classes of nodes and connections allowed only across but not
within the two classes. Surprisingly, current complex network theory presents a
theoretical bottle-neck: a general framework for local-based link prediction
directly in the bipartite domain is missing. Here, we overcome this theoretical
obstacle and present a formal definition of common neighbour index (CN) 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. Our
models significantly improve topological prediction in many bipartite networks
because they exploit local physical driving-forces that participate in the
formation and organization of many 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.
