Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature of Hypergraphs via Multi-Marginal Optimal Transport   We introduce a novel definition of curvature for hypergraphs, a natural
generalization of graphs, by introducing a multi-marginal optimal transport
problem for a naturally defined random walk on the hypergraph. This curvature,
termed \emph{coarse scalar curvature}, generalizes a recent definition of Ricci
curvature for Markov chains on metric spaces by Ollivier [Journal of Functional
Analysis 256 (2009) 810-864], and is related to the scalar curvature when the
hypergraph arises naturally from a Riemannian manifold. We investigate basic
properties of the coarse scalar curvature and obtain several bounds. Empirical
experiments indicate that coarse scalar curvatures are capable of detecting
"bridges" across connected components in hypergraphs, suggesting it is an
appropriate generalization of curvature on simple graphs.

21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio