Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models

Humphries, Mark D.; Caballero, Javier A.; Evans, Mat; Maggi, Silvia; Singh, Abhinav

Abstract

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network's low-dimensional structure, and the nodes that participate in it, using any null model. We use generative models to estimate the expected eigenvalue distribution under a specified null model, and then detect where the data network's eigenspectra exceed the estimated bounds. On synthetic networks, this spectral estimation approach cleanly detects transitions between random and community structure, recovers the number and membership of communities, and removes noise nodes. On real networks spectral estimation finds either a significant fraction of noise nodes or no departure from a null model, in stark contrast to traditional community detection methods. Across all analyses, we find the choice of null model can strongly alter conclusions about the presence of network structure. Our spectral estimation approach is therefore a promising basis for detecting low-dimensional structure in real-world networks, or lack thereof.

Citation

Humphries, M. D., Caballero, J. A., Evans, M., Maggi, S., & Singh, A. (2021). Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models. PLoS ONE, 16(7), Article e0254057. https://doi.org/10.1371/journal.pone.0254057

• Journal Article Type: Article
• Acceptance Date: Jun 24, 2021
• Online Publication Date: Jul 2, 2021
• Publication Date: Jul 2, 2021
• Deposit Date: Jun 29, 2021
• Publicly Available Date: Jul 5, 2021
• Journal: PLoS ONE
• Electronic ISSN: 1932-6203
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Issue: 7
• Article Number: e0254057
• DOI: https://doi.org/10.1371/journal.pone.0254057
• Keywords: General Biochemistry, Genetics and Molecular Biology; General Agricultural and Biological Sciences; General Medicine
• Public URL: https://nottingham-repository.worktribe.com/output/5746144
• Publisher URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0254057