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.