Modularity clustering is force-directed layout
Open accessAbstract
Two natural and widely used representations for the community structure of networks are clusterings, which partition the vertex set into disjoint subsets, and layouts, which assign the vertices to positions in a metric space. This paper unifies prominent characterizations of layout quality and clustering quality, by showing that energy models of pairwise attraction and repulsion subsume Newman and Girvan's modularity measure. Layouts with optimal energy are relaxations of, and are thus consistent with, clusterings with optimal modularity, which is of practical relevance because the two representations are complementary and often used together.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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?
Several studies argue that a democracy needs deliberation, and polarization enables such deliberation to happen in the public to a certain extent, informing people about issues and arguments from different sides.
“Several studies [11,42] argue that a democracy needs deliberation, and polarization enable such a deliberation to happen in the public, to a certain extent, thus informing people about the issues and arguments from different sides.”
From Quantifying controversy on social media (2018) · cites this paper as [42]
The Introduction (p. 1) discusses communities in networks, and the Examples section (p. 7) uses politically classified books to illustrate a network layout. Neither addresses whether democracy needs deliberation or whether polarization enables public deliberation; searches for those concepts found no relevant passage. (LLM, conf=0.78)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Finding and evaluating community structure in networks
Newman, M. E. J., & Girvan, M. (2004) · Physical Review E · doi:10.1103/physreve.69.026113 · Cited by 13,931 · see citing works
Modularity and community structure in networks
Newman, M. E. J. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0601602103 · Cited by 12,256 · see citing works
Resolution limit in community detection
Fortunato, S., & Barthélemy, M. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0605965104 · Cited by 3,024 · see citing works
Flagged first, then by citations
Research works printed but not linked: 10
- [22]R. Rotta, Diploma thesis, Brandenburg University of Technology (2008), URL http://www.informatik.tu-cottbus.de/ ~ rrotta/ .
- [23]R. Diestel, Graph Theory (Springer, New York, 2000), 2nd ed.
- [25]S. Fortunato and M. Barth´ elemy, Proc. Natl. Acad. Sci. U.S.A. 104 , 36 (2007).
- [27]A. Noack, in Proceedings of the 13th International Symposium on Graph Drawing (GD 2005) , edited by P. Healy and N. S. Nikolov (Springer, Berlin, 2006), LNCS 3843, pp. 309-320.
- [29]J. D. Carroll and S. Pruzansky, in Similarity and Choice: Papers in Honour of Clyde Coombs , edited by E. D. Lantermann and H. Feger (Huber, Bern, 1980), pp. 108139.
- [15]A. Noack, Ph.D. thesis, Brandenburg University of Technology (2007), URL http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus-4046
- [30]S. White and P. Smyth, in Proceedings of the 5th SIAM International Conference on Data Mining (SDM 2005) (SIAM, Philadelphia, 2005), pp. 274-285.
- [34]S. Arora, S. Rao, and U. V. Vazirani, in Proceedings of the 36th ACM Symposium on Theory of Computing (STOC 2004) , edited by L. Babai (ACM, New York, 2004), pp. 222-231.
- [36]M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 103 , 8577 (2006).
- [41]M. Gaertler, R. G¨ orke, and D. Wagner, in Proceedings of the 3rd International Conference on Algorithmic Aspects in Information and Management (AAIM 2007) , edited by M.-Y. Kao and X.-Y. Li (Springer, Berlin, 2007), LNCS 4508, pp. 11-26. http://code.google.com/p/linloglayout/ http://code.google.com/p/linloglayout/
Cited by
Sorted by citations
Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293 · see citing works
Jacomy, M., Venturini, T., Heymann, S., & Bastian, M. (2014) · PLoS ONE · doi:10.1371/journal.pone.0098679 · Cited by 2,909 · see citing works
Systematic Literature Review on the Spread of Health-related Misinformation on Social Media
Wang, Y., McKee, M., Torbica, A., & Stuckler, D. (2019) · Social Science & Medicine · doi:10.1016/j.socscimed.2019.112552 · Cited by 1,806 · see citing works
Quantifying controversy on social media
Garimella, K., Morales, G. D. F., Gionis, A., & Mathioudakis, M. (2018) · ACM Transactions on Social Computing · doi:10.1145/3140565 · Cited by 348 · see citing works
Mapping the Research Landscape of Nature-Based Solutions in Urbanism
Li, L., Cheshmehzangi, A., Chan, F. K. S., & Ives, C. D. (2021) · Sustainability · doi:10.3390/su13073876 · Cited by 71 · see citing works
- Authors
- Noack, A.
- Affiliations
- Brandenburg University of Technology Cottbus-Senftenberg (DE)
- Corresponding author
- Noack, Andreas
- ORCID
- Noack, Andreas
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2009-02-02
- Volume
- 79
- Issue
- 2
- Pages
- 026102-026102
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2047583926
- Cited by
- 258
- References
- 3
- Citations by year
- 2026: 6 · 2025: 13 · 2024: 11 · 2023: 27 · 2022: 17 · 2021: 23 · 2020: 14 · 2019: 21 · 2018: 18 · 2017: 12 · 2016: 18 · 2015: 15 · 2014: 14 · 2013: 14 · 2012: 10
- FWCI
- 7.80
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Clustering Algorithms Research
- Physical Sciences › Mathematics › Geometry and Topology › Graph theory and applications
- Keywords
- modularity, community structure, force-directed layout, network clustering, energy model, clustering quality
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
