Unveiling Signed Complexity: A Statistically Validated Bipartite Projection

Bipartite networks provide a fundamental insight into the organisation of complex real-world systems. A key challenge in modeling these systems is devising a monopartite projection that preserves the intricate information encoded within the original bipartite structure. We propose an unsupervised algorithm to obtain statistically validated projections of bipartite signed networks, according to which any two nodes sharing a statistically significant number of concordant (discordant) motifs are connected by a positive (negative) edge. By assessing statistical significance through four distinct Exponential Random Graph Models (ERGMs), we generate link-specific p-values filtered via multiple testing correction. After validating the method on synthetic configurations from a fully controllable generative model, we apply it to three real-world social networks. In all cases, the algorithm detects non-trivial mesoscopic structures that cannot be explained by the constraints of the null models, thus unveiling the authentic signed complexity of the underlying system. Finally, we show how the inherent flexibility of our framework allows for easy extensions to more sophisticated null models and different complex systems.