On λ-Forman-Ricci curvature of networks | RAIRO

Open Access

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

R. Aguilar-Sanchez, I.F. Herrera-Gonzalez, J.A. Mendez-Bermudez and J.M. Sigarreta, Computational properties of general indices on random networks. Symmetry 12 (2020) 1341. [Google Scholar]
R. Aguilar-Sanchez, J.A. Mendez-Bermudez, J.M. Rodríguez and J.M. Sigarreta, Normalized Sombor indices as complexity measures of random networks. Entropy 23 (2021) 976. [Google Scholar]
R. Aguilar-Sanchez, I.F. Herrera-Gonzalez, J.A. Mendez-Bermudez and J.M. Sigarreta, Revan-degree indices on random graphs. Preprint arXiv:2210.04749 (2022). [Google Scholar]
R. Aguilar-Sanchez, J.A. Mendez-Bermudez, J.M. Rodríguez and J.M. Sigarreta, Multiplicative topological indices: Analytical properties and application to random networks. AIMS Math. 9 (2024) 3646. [Google Scholar]
V. Alvarez, A. Portilla, J.M. Rodríguez and E. Tourís, Gromov hyperbolicity of Denjoy domains. Geom. Dedicata 121 (2006) 221–245. [Google Scholar]
V. Barkanass, J. Jost and E. Saucan, Geometric sampling of networks. J. Complex Netw. 10 (2022) cnac014. [Google Scholar]
S. Bermudo, J.M. Rodríguez, J.M. Sigarreta and J.-M. Vilaire, Gromov hyperbolic graphs. Discr. Math. 313 (2013) 1575–1585. [Google Scholar]
A. Cantón, J.L. Fernández, D. Pestana and J.M. Rodríguez, On harmonic functions on trees. Poten. Anal. 15 (2001) 199–244. [Google Scholar]
R. Cruz, I. Gutman and J. Rada, Sombor index of chemical graphs. Appl. Math. Comput. 399 (2021) 126018. [Google Scholar]
J. Dall and M. Christensen, Random geometric graphs. Phys. Rev. E 66 (2002) 016121. [Google Scholar]
K. Devriendt and R. Lambiotte, Discrete curvature on graphs from the effective resistance. J. Phys. Complexity 3 (2022) 025008. [Google Scholar]
P. Erdös and A. Rényi, On random graphs. Publ. Math. (Debrecen) 6 (1959) 290–297. [Google Scholar]
P. Erdös and A. Rényi, On the evolution of random graphs. Inst. Hung. Acad. Sci. 5 (1960) 17–61. [Google Scholar]
P. Erdös and A. Rényi, On the strength of connectedness of a random graph. Acta Math. Hungar. 12 (1961) 261–267. [Google Scholar]
E. Estrada and M. Sheerin, Random rectangular graphs. Phys. Rev. E 91 (2015) 042805. [Google Scholar]
L. Fesser, S. Serrano de Haro Iváñez, K. Devriendt, M. Weber and R. Lambiotte, Augmentations of Forman’s Ricci curvature and their applications in community detection. J. Phys.: Complexity 5 (2024) 035010. [Google Scholar]
R. Forman, Bochner’s method for cell complexes and combinatorial Ricci curvature. Discr. Comput. Geom. 29 (2003) 323–374. [Google Scholar]
E.N. Gilbert, Random graphs. Ann. Math. Stat. 30 (1959) 1141. [Google Scholar]
A. Granados, D. Pestana, A. Portilla, J.M. Rodríguez and E. Tourís, Stability of the injectivity radius under quasi-isometries and applications to isoperimetric inequalities. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM 112 (2018) 1225–1247. [Google Scholar]
A. Granados, D. Pestana, A. Portilla, J.M. Rodríguez and E. Tourís, Stability of the volume growth rate under quasi-isometries. Rev. Mat. Complut. 33 (2020) 231–270. [Google Scholar]
A. Granados, D. Pestana, A. Portilla and J.M. Rodríguez, Stability of p-parabolicity under quasi-isometries. Math. Nachr. 295 (2022) 536–559. [Google Scholar]
A. Granados, D. Pestana, A. Portilla, J.M. Rodríguez and E. Tourís, Liouville property and quasi-isometries on negatively curved Riemannian surfaces. Proc. R. Soc. Edinburgh 154 (2024) 131–153. [Google Scholar]
A. Granados, A. Portilla, J.M. Rodríguez and E. Tourís, Liouville property and quasi-isometries on non-positively curved Riemannian surfaces. Math. Nachr. 298 (2025) 794–805. [Google Scholar]
I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17 (1972) 535–538. [CrossRef] [Google Scholar]
I. Gutman, J. Rada and O. Araujo, The wiener index of starlike trees and a related partial order. MATCH Commun. Math. Comp. Chem. 42 (2000) 145–154. [Google Scholar]
I. Holopainen and P.M. Soardi, p-harmonic functions on graphs and manifolds. Manuscr. Math. 94 (1997) 95–110. [Google Scholar]
I. Holopainen and P.M. Soardi, A strong Liouville theorem for p-harmonic functions on graphs. Ann. Acad. Sci. Fenn. 22 (1997) 205–226. [Google Scholar]
S.S.D.H. Iváñez, Comparative analysis of Forman-Ricci curvature versions applied to the persistent homology of networks. arXiv:2212.01357 (2022). [Google Scholar]
J. Jost and S. Liu, Ollivier’s Ricci curvature, local clustering and curvature-dimension inequalities on graphs. Discrete Comput. Geom. 51 (2014) 300–322. [Google Scholar]
M. Kanai, Rough isometries and combinatorial approximations of geometries of non-compact Riemannian manifolds. J. Math. Soc. Jpn. 37 (1985) 391–413. [Google Scholar]
H. Li, J. Cao, J. Zhu, Y. Liu, Q. Zhu and G. Wu, Curvature graph neural network. Inf. Sci. 592 (2022) 50–66. [Google Scholar]
C.T. Martinez-Martinez, J.A. Mendez-Bermudez, Y. Moreno, J.J. Pineda-Pineda and J.M. Sigarreta, Spectral and localization properties of random bipartite graphs. Chaos Soliton Fractals X 3 (2019) 100021. [Google Scholar]
Y. Ollivier, Ricci curvature of metric spaces. C. R. Acad. Sci. Paris 345 (2007) 643–646. [Google Scholar]
Y. Ollivier, Ricci curvature of Markov chains on metric spaces. J. Funct. Anal. 256 (2009) 810–864. [Google Scholar]
M. Penrose, Random Geometric Graphs. Oxford University Press, Oxford (2003). [Google Scholar]
J.M. Rodríguez and E. Tourís, A new characterization of Gromov hyperbolicity for negatively curved surfaces. Publ. Mat. 50 (2006) 249–278. [Google Scholar]
A. Samal, R.P. Sreejith, J. Gu, S. Liu, E. Saucan and J. Jost, Comparative analysis of two discretizations of Ricci curvature for complex networks. Sci. Rep. 8 (2018) 1–16. [Google Scholar]
E. Saucan, R.P. Sreejith, R.P. Vivek-Ananth, J. Jost and A. Samal, Discrete Ricci curvatures for directed networks. Chaos Solitons Fractals 118 (2019) 347–360. [Google Scholar]
Y. Shang, Lack of Gromov-hyperbolicity in colored random networks. Pan-Am. Math. J. 21 (2011) 27–36. [Google Scholar]
Y. Shang, Lack of Gromov-hyperbolicity in small-world networks. Cent. Eur. J. Math. 10 (2012) 1152–1158. [CrossRef] [MathSciNet] [Google Scholar]
Y. Shang, Non-hyperbolicity of random graphs with given expected degrees. Stoch. Models. 29 (2013) 451–462. [Google Scholar]
P.M. Soardi, Potential Theory in Infinite Networks. Lecture Notes in Mathematics. Vol. 1590. Springer-Verlag (1994). [Google Scholar]
R. Solomonoff and A. Rapoport, Connectivity of random nets. Bull. Math. Biophys. 13 (1951) 107–117. [Google Scholar]
B. Tadic, Self-organised criticality and emergent hyperbolic networks: blueprint for complexity in social dynamics. Eur. J. Phys. 40 (2019) 024002. [Google Scholar]
B. Tadic, M. Andjelkovic, and R. Melnik, Functional geometry of human connectomes. Sci. Rep. 9 (2019) 12060. [Google Scholar]
E. Tu, L. Cao, J. Yang and N. Kasabov, A novel graph-based k-means for nonlinear manifold clustering and representative selection. Neurocomputing 143 (2014) 109–122. [Google Scholar]
D.J. Watts and S.H. Strogatz, Collective dynamics of small-world networks. Nature 393 (1988) 440–442. [Google Scholar]
M. Weber, E. Saucan and J. Jost, Characterizing complex networks with Forman-Ricci curvature and associated geometric flows. J. Complex Netw. 5 (2017) 527–550. [Google Scholar]
M. Weber, E. Saucan and J. Jost, Coarse geometry of evolving networks. J. Complex Netw. 6 (2018) 706–732. [Google Scholar]
Y. Wu and C. Zhang, Hyperbolicity and chordality of a graph. Electr. J. Comb. 18 (2011) P43. [Google Scholar]
Y. Zhang, J. Mańdziuk, C.H. Quek and B.W. Goh, Curvature-based method for determining the number of clusters. Inf. Sci. 415–416 (2017) 414–428. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.