For r-uniform linear hypergraphs with nonnegative Lin-Lu-Yau curvature, edge-connectivity equals minimum incidence degree, while nonlinear examples violate this with arbitrarily large gaps.
Lin-Lu-Yau Ricci curvature on hypergraphs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, we introduce a unified framework for defining Lin-Lu-Yau (LLY) Ricci curvature on both undirected and directed hypergraphs. By establishing upper bounds and monotonicity properties for the parameterized curvature $\kappa_\alpha$, we justify the well-posedness and compatibility of our definitions. Furthermore, we prove a Bonnet-Myers-type theorem for hypergraphs, which highlights the potential of LLY Ricci curvature in hypergraph analysis, particularly in studying geometric and structural properties. Our results extends the foundational definitions of graph Ricci curvature by Ollivier and Lin-Lu-Yau to the hypergraph setting.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2026 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Edge-connectivity and LLY curvature of hypergraphs
For r-uniform linear hypergraphs with nonnegative Lin-Lu-Yau curvature, edge-connectivity equals minimum incidence degree, while nonlinear examples violate this with arbitrarily large gaps.