Melanie Weber, Emil Saucan, Jürgen Jost (2016), Journal of Complex Networks 5, 527-550 (2017); first posted as arXiv preprint — ARXIV-1607.08654
Key takeaways
- Forman’s combinatorial discretization of Ricci curvature gives a cheap, edge-based network characteristic whose distribution separates model network classes (real networks resemble Barabasi-Albert) and whose associated Ricci and Laplacian flows can be used for change detection and denoising in evolving weighted networks.
Seeded from the abstract and a skim, before the reading in NOTE-026. What follows is what the work says about itself.
The paper proposes Forman-Ricci curvature, and the geometric flow built on it, as edge-level descriptors of complex networks to complement the usual node-based statistics. After motivating the construction mathematically, the authors compute these quantities on static and time-evolving networks and compare them with established node-degree-based measures. They argue the tools could support data-mining tasks such as denoising, clustering, and extrapolating how a network evolves.
Standing in the record
Filed by the reading-time triage of 2026-09-25: 1,790 seconds of active reading over 3 sessions in the papers-feed tracker. It was filed Deferred, unread. NOTE-026 is the close reading of 2026-09-25, and it placed the work: Active — the standard early citation for Forman–Ricci curvature on networks and for the Forman–Ricci flow. Read it for §2.3 (Eqs. 11–17) and §4.1 (Eqs. 36–41), and cite it for definitions only. Its empirical and application claims are one-table or one-figure demonstrations. Several of its formulas contain sign and consistency slips, listed below, so a user should take Eq. 11 from here and check it against Sreejith et al. 2016.
When seeded, before the reading in NOTE-026, the entry gave a priority for a deeper reading: medium — frequently cited foundational source for Forman curvature on networks and the owner spent ~30 min (t=1790 s); the skim captures the constructions, but the curvature formula and flow definitions (§2.3, §4) are worth a careful pass if graph curvature is being used downstream.
What the seeding asked a deeper reading to check (NOTE-026 is that reading):
- The practical claim (Forman ~ Ollivier at a fraction of the cost) is asserted with “strong indications” and deferred to a forthcoming study; verify against later comparison papers before relying on it.
- Empirical evidence is small (three real networks, three models); the “classification scheme” is demonstrated on a handful of samples.
- ML link: discrete Ricci curvature (Forman and variants) later became a tool for diagnosing over-squashing and guiding graph rewiring in GNNs; this paper is an early network-science source for Forman curvature on graphs, not for those GNN results themselves.
Access when seeded: arXiv abs page and full v2 PDF (29 pp., “extended version”) read via arxiv.org. The arXiv page gives no DOI (comment says “To appear in: Journal of Complex Networks”); the DOI was matched through a Crossref bibliographic search (same title, authors Weber/Saucan/Jost, J. Complex Networks vol. 5 pp. 527-550, online 2017-01-16). Keywords are taken verbatim from the line after the abstract in the PDF. Supplemental Material (implementation details) not read.