Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs
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| Format: | Preprint |
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2026
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| author | Ding, Hao Krishnagopal, Sanjukta |
| author_facet | Ding, Hao Krishnagopal, Sanjukta |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs Ding, Hao Krishnagopal, Sanjukta Physics and Society Social and Information Networks Quantitative Methods 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. |
| title | Sparse Contextual Coupling Reshapes Diffusion Geometry in Multilayer Hypergraphs |
| topic | Physics and Society Social and Information Networks Quantitative Methods |
| url | https://arxiv.org/abs/2605.20454 |