Common neighbours and the local-community-paradigm for 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 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.

💡 Research Summary

The paper addresses a fundamental gap in network science: the lack of a principled, local‑based link‑prediction framework that operates directly on bipartite graphs. Bipartite networks consist of two disjoint node sets (often called “top” and “bottom” nodes) where edges are allowed only across the sets. Existing link‑prediction methods—such as Common Neighbours (CN), Adamic‑Adar, Preferential Attachment, and many community‑aware scores—are defined for unipartite (single‑mode) graphs. When applied to bipartite data they either require a projection onto a unipartite graph (which discards crucial structural information) or they are simply inapplicable.

Theoretical contribution
The authors first give a rigorous definition of the Common Neighbour index for bipartite graphs. In a bipartite setting, a “common neighbour” of a top node u and a bottom node v is a node w of the opposite type that is simultaneously adjacent to both u and v. Formally,

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