Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-way dual Cheeger constants and spectral bounds of graphs   We introduce a set of multi-way dual Cheeger constants and prove universal
higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace
operators on weighted finite graphs. Our proof proposes a new spectral
clustering phenomenon deduced from metrics on real projective spaces. We
further extend those results to a general reversible Markov operator and find
applications in characterizing its essential spectrum.

27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn