Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs

TL;DR

This paper presents a diffusion-based framework for analyzing how sparse, condition-specific layers reshape the diffusion geometry in multilayer hypergraphs, with applications to disease-related gene networks.

Contribution

The paper introduces a novel diffusion-based method to study the influence of sparse layers on multilayer hypergraph geometry, revealing significant structural effects in biological networks.

Findings

Sparse disease-specific gene layers significantly alter diffusion distances.

Community structures reflect disease-specific functional enrichments.

Disease similarities are identified beyond direct gene overlap.

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.