Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs
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.
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BibTeX
@misc{ding2026sparse,
title = {{Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs}},
author = {Hao Ding and Sanjukta Krishnagopal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.20454},
eprint = {2605.20454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.20454},
}
RIS
TY - UNPB
TI - Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs
AU - Hao Ding
AU - Sanjukta Krishnagopal
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2605.20454
UR - https://arxiv.org/abs/2605.20454
AB - 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.
ER -