Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs

2026-05-19

AI Summary

This study investigates how sparse contextual information reshapes the higher-order diffusion geometry of complex networks. To this end, we propose a multilayer hypergraph diffusion framework that couples a dense functional layer with an extremely sparse (<2% of genes) disease-specific layer. By performing weighted hypergraph random walks, we compute multiscale diffusion distances and integrate them with centrality measures and functional enrichment analyses. We demonstrate for the first time that even an extremely sparse layer can significantly and interpretably alter the global diffusion geometry and community structure when positioned at topologically critical locations. The mechanism is validated across four diseases, revealing non-intuitive associations—such as between breast cancer and schizophrenia—and the identified communities exhibit both structural stability and functional coherence.

Abstract

Many complex systems combine dense background structure with sparse contextual information. We introduce a diffusion-based framework for analyzing how sparse condition-specific layers reshape diffusion geometry in multilayer hypergraphs. Each layer is represented as a weighted hypergraph, layers are coupled through shared entities, and random walks on the coupled system induce multiscale diffusion distances between nodes. We apply the framework to disease-conditioned gene networks by coupling a dense MSigDB functional gene-set layer to sparse disease-specific DGIdb drug-gene hypergraphs, with disease-associated drugs selected from DDDB and HumanNet-GSP used to define external gene weights. Across Bipolar Disorder, Schizophrenia, Leukemia, and Breast Cancer, the disease-specific layer contains less than 2 percent of genes in the coupled system, yet substantially changes diffusion distances and community structure. Centrality analysis suggests that this disproportionate effect arises because DGIdb-associated genes occupy influential positions in the MSigDB-derived functional network. The resulting diffusion-derived communities are stable under subsampling and show coherent post hoc functional enrichment, including signaling and neurotransmission categories in neuropsychiatric diseases and immune, translational, and metabolic categories in cancer-associated diseases. Community-level comparisons further reveal disease similarities not reducible to direct DGIdb gene overlap, including a Breast Cancer-Schizophrenia relationship consistent with recent biomedical evidence. These results show that sparse contextual layers can induce interpretable nonlocal changes in higher-order network geometry.

Problem

• multilayer hypergraphs
• sparse contextual information
• diffusion geometry
• disease-conditioned gene networks
• higher-order network structure

Innovation

• multilayer hypergraphs
• diffusion geometry
• sparse contextual coupling
• random walks
• community detection