Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing the second smallest eigenvalue of the normalized
  Laplacian of a tree   In this paper we show a monotonicity theorem for the harmonic eigenfunction
of \lambda_{1} of the normalized Laplacian over the points of articulation of a
graph. We introduce the definition of Perron component for the normalized
Laplacian matrix of a graph and show how its second smallest eigenvalue can be
characterized using this definition.

21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an