ArticleNature communications2021
Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature.
Article in Nature communications, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
6 citing papers in PubMed.
- MARBLE: interpretable representations of neural population dynamics using geometric deep learning.Nature methods · 2025Article
- ATP-dependent thermoring basis for the heat unfolding of the first nucleotide-binding domain isolated from human CFTR.Research square · 2024Article
- Multi-scale geometric network analysis identifies melanoma immunotherapy response gene modules.Scientific reports · 2024Article
- Dynamic network curvature analysis of gene expression reveals novel potential therapeutic targets in sarcoma.Scientific reports · 2024Article
- Multi-Scale Geometric Network Analysis Identifies Melanoma Immunotherapy Response Gene Modules.bioRxiv : the preprint server for biology · 2023Article
- Community detection in networks by dynamical optimal transport formulation.Scientific reports · 2022Article
Corrections and comments
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Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to specific classes of networks because incompatible metric spaces generally result in information loss. Here, we study arbitrary networks geometrically by defining a dynamic edge curvature measuring the similarity between pairs of dynamical network processes seeded at nearby nodes. We show that the evolution of the curvature distribution exhibits gaps at characteristic timescales indicating bottleneck-edges that limit information spreading. Importantly, curvature gaps are robust to large fluctuations in node degrees, encoding communities until the phase transition of detectability, where spectral and node-clustering methods fail. Using this insight, we derive geometric modularity to find multiscale communities based on deviations from constant network curvature in generative and real-world networks, significantly outperforming most previous methods. Our work suggests using network geometry for studying and controlling the structure of and information spreading on networks.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.