Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectrum of the normalized graph Laplacian   The spectrum of the normalized graph Laplacian yields a very comprehensive
set of invariants of a graph. In order to understand the information contained
in those invariants better, we systematically investigate the behavior of this
spectrum under local and global operations like motif doubling, graph joining
or splitting. The eigenvalue 1 plays a particular role, and we therefore
emphasize those constructions that change its multiplicity in a controlled
manner, like the iterated duplication of nodes.

4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex