Hyperpathway: visualizing organization of pathway-molecule enriched interactions in omics studies via hyperbolic bipartite network embedding.

Pathway enrichment analysis (PEA) of omics data identifies significant pathway–molecule associations, yet delivers results as tabular lists in which complex systems-biology insights remain inaccessible. Hyperpathway is an open-access network-based webtool that addresses this limitation through three original innovations: (1) conversion of a PEA results table into a pathway–molecule bipartite network; (2) a minimal artificial linking strategy to resolve structural disconnections; (3) a leaf removal and post-hoc reinsertion pipeline that accelerates coalescent embedding without any loss of geometric fidelity. The resulting network is visualized in a two-dimensional hyperbolic disk with flexible coloring schemes encoding hierarchical relevance, connectivity similarity, statistical significance, or user-defined annotations; revealing latent functional modules that are invisible in conventional tabular outputs. Validated on genomic, metabolomic, and lipidomic datasets, Hyperpathway enables a deeper, systems-level understanding of the interplay between pathways and their molecular components, providing insights that go beyond p-value-based significance testing. Beyond PEA, Hyperpathway can be used as a general-purpose open webtool for fast hyperbolic embedding and interactive visualization of any bipartite network.