Extracting the transitivity backbone of bipartite networks.

Real bipartite networks combine degree-constrained random mixing with structured connectivity balancing short and long range connections, effectively accounted for by geometric network models. We introduce a statistical filter that benchmarks node-level bipartite clustering against degree-preserving randomizations to classify nodes as geometric (signal) or degree constrained noise. In synthetic mixtures with known ground truth, the filter achieves high classification accuracy and sharpens inference of latent geometric parameters. Applied to four empirical systems -metabolism, online group membership, plant-pollinator interactions, and languages- the filter isolates recurrent neighborhoods while removing ubiquitous or weakly co-occurring entities. Filtering exposes a compact geometric backbone that disproportionately sustains connectivity under percolation and preserves downstream classifier accuracy in node-feature tasks, offering a simple, scalable way to disentangle structure from noise in bipartite networks.