Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating Spectral Impact of Structural Perturbations in Large
  Networks   Determining the effect of structural perturbations on the eigenvalue spectra
of networks is an important problem because the spectra characterize not only
their topological structures, but also their dynamical behavior, such as
synchronization and cascading processes on networks. Here we develop a theory
for estimating the change of the largest eigenvalue of the adjacency matrix or
the extreme eigenvalues of the graph Laplacian when small but arbitrary set of
links are added or removed from the network. We demonstrate the effectiveness
of our approximation schemes using both real and artificial networks, showing
in particular that we can accurately obtain the spectral ranking of small
subgraphs. We also propose a local iterative scheme which computes the relative
ranking of a subgraph using only the connectivity information of its neighbors
within a few links. Our results may not only contribute to our theoretical
understanding of dynamical processes on networks, but also lead to practical
applications in ranking subgraphs of real complex networks.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg