Metraipolis › archive › dc_efa4fa124ba2

Ollivier's Ricci Curvature on Complex-weighted Graphs — arXiv:2608.10132

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.10132
License (as archived): CC0-1.0
Archived: 2026-10-19T06:16:00.003Z
SHA-256 of the archived text: e146328d2708ce9bc5967daecf488fc88b12dde0999e107acef7e318ffa13e0c
Stable URL of this page: https://metraipolis.com/documento/dc_efa4fa124ba2

How to cite

Ollivier's Ricci Curvature on Complex-weighted Graphs — arXiv:2608.10132 — arXiv (en), https://arxiv.org/abs/2608.10132 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_efa4fa124ba2 (Metraipolis archive dc_efa4fa124ba2, sha256 e146328d2708ce9bc5967daecf488fc88b12dde0999e107acef7e318ffa13e0c)

BibTeX

@misc{dcefa4fa124ba2,
  title = {Ollivier's Ricci Curvature on Complex-weighted Graphs — arXiv:2608.10132},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.10132},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_efa4fa124ba2; sha256 e146328d2708ce9bc5967daecf488fc88b12dde0999e107acef7e318ffa13e0c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.10132. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Understanding the geometry of complex networks is critical for effective modeling and analysis across domains. While discrete notions of Ricci curvature have emerged as powerful tools for characterizing both local and global network structure, existing formulations are largely confined to undirected networks with real-valued weights. This limits the use of curvature-based analysis of directional and complex-weighted relations that arise naturally in many applications, from social and biological systems to quantum and signal-processing networks. In this work, we introduce a principled extension of Ollivier's Ricci curvature to complex-weighted graphs, which encompasses directed graphs as a special case. We establish fundamental theoretical properties of this new notion, including relations to the magnetic Laplacian and combinatorial upper and lower bounds that relate curvature to cycle structure in local neighborhoods. We further develop computational methods for curvature estimation and demonstrate their utility in community detection on directed networks.

Tema degli esploratori: governance digitale e beni comuni (retro-catalogo arXiv: annunci del 2026-08-12 in cs.SI).
Categorie arXiv: Social and Information Networks (cs.SI) ; Metric Geometry (math.MG); Physics and Society (physics.soc-ph).
Pagina del lavoro: https://arxiv.org/abs/2608.10132 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T06:10:53.159Z dalla pagina https://arxiv.org/catchup/cs.SI/2026-08-12?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).