Laplacians and the Cheeger Inequality for Directed Graphs
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The modules in Fig. 2 were obtained with the Louvain algorithm, and similar modules are obtained when spectral clustering is used.
“The modules in Fig. 2 were obtained with the Louvain algorithm for graph clustering38, which is designed to maximize modularity. Similar modules are obtained when spectral clustering39 is used”
From Predicting modular functions and neural coding of behavior from a synaptic wiring diagram (2024) · cites this paper as [39]
Cited by
Sorted by citations
Online Social Spammer Detection
Hu, X., Tang, J., & Liu, H. (2014) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v28i1.8728 · Cited by 133 · see citing works
Improving Graph Attention Networks with Large Margin-based Constraints
Wang, G., Ying, R., Huang, J., & Leskovec, J. (2019) · arXiv · doi:10.48550/arxiv.1910.11945 · Cited by 61 · see citing works
On the Linear Convergence of Distributed Optimization over Directed Graphs
Xi, C., & Khan, U. A. (2015) · arXiv · doi:10.48550/arxiv.1510.02149 · Cited by 29 · see citing works
Magnetic Eigenmaps for the visualization of directed networks
Fanuel, M., Alaíz, C. M., Fernández, Á., & Suykens, J. A. K. (2018) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2017.01.004 · Cited by 35 · see citing works
Predicting modular functions and neural coding of behavior from a synaptic wiring diagram
Vishwanathan, A., Sood, A., Wu, J., Ramirez, A. D., Yang, R., Kemnitz, N., Ih, D., Turner, N., Lee, K., Tartavull, I., et al. (2024) · Nature Neuroscience · doi:10.1038/s41593-024-01784-3 · Cited by 25 · see citing works
“We used a generalized spectral clustering algo-rithm for weighted directed graphs to bisect the zebrafish ‘center’ sub-graph, as proposed by Chung 39 .”
Which digraphs with ring structure are essentially cyclic?
Agaev, R., & Chebotarev, P. (2010) · Advances in Applied Mathematics · doi:10.1016/j.aam.2010.01.005 · Cited by 11 · see citing works
- Authors
- Chung, F.
- Affiliations
- University of California San Diego (US)
- Corresponding author
- Chung, Fan
- ORCID
- Chung, Fan
- Venue
- Annals of Combinatorics
- Published
- 2005-04
- Volume
- 9
- Issue
- 1
- Pages
- 1-19
- ISSN
- 0218-0006 (ISSN-L)
- 0219-3094
- OpenAlex
- W2069992656
- Cited by
- 535
- References
- 0
- Citations by year
- 2026: 19 · 2025: 19 · 2024: 27 · 2023: 20 · 2022: 27 · 2021: 37 · 2020: 41 · 2019: 35 · 2018: 30 · 2017: 32 · 2016: 41 · 2015: 35 · 2014: 27 · 2013: 20 · 2012: 18
- FWCI
- 23.25
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Annals of Combinatorics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Graph theory and applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- directed graphs, graph Laplacian, Cheeger inequality, Cheeger constant, eigenvalues, circulation, Rayleigh quotient, non-reversible Markov chains, convergence rate, comparison theorems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
