| Issue |
RAIRO-Oper. Res.
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 3729 - 3747 | |
| DOI | https://doi.org/10.1051/ro/2025124 | |
| Published online | 19 December 2025 | |
On λ-Forman-Ricci curvature of networks
1
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
2
Universidad Carlos III de Madrid, ROR: https://ror.org/03ths8210, Departamento de Matemáticas, Avenida de la Universidad, 30 (edificio Sabatini), 28911 Leganés, ( Madrid), Spain
3
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. 54 Col. Garita, 39650 Acalpulco, Guerrero, Mexico
* Corresponding author: jsmathguerrero@gmail.com
Received:
25
August
2024
Accepted:
8
September
2025
Several discrete versions of Ricci curvature have been proposed since the geometrical properties of a network are used to understand important information associated with it. In this paper we obtain the main properties of the λ-Forman-Ricci curvature, a concept that generalizes and integrates the Forman-Ricci curvature and the augmented Forman-Ricci curvature. We show that this definition captures the essence of Ricci curvature in Riemannian manifolds, by proving discrete analogues of important results in geometry. Also, we study the integral λ-Forman-Ricci curvature, obtaining a kind of Gauss–Bonnet formula, and we study this integral curvature in the context of random networks.
Mathematics Subject Classification: 05C07 / 05C38 / 05C80
Key words: λ-Forman-Ricci curvature / integral λ-Forman-Ricci curvature / random networks
© The authors. Published by EDP Sciences, ROADEF, SMAI 2025
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