Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectrally positive Bakry-\'Emery Ricci curvature on graphs   We investigate analytic and geometric implications of non-constant Ricci
curvature bounds. We prove a Lichnerowicz eigenvalue estimate and finiteness of
the fundamental group assuming that $L+2 Ric$ is a positive operator where $L$
is the graph Laplacian. Assuming that the negative part of the Ricci curvature
is small in Kato sense, we prove diameter bounds, elliptic Harnack inequality
and Buser inequality. This article seems to be the first one establishing these
results while allowing for some negative curvature.

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph