Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring the Robustness of Graph Properties   In this paper, we propose a perturbation framework to measure the robustness
of graph properties. Although there are already perturbation methods proposed
to tackle this problem, they are limited by the fact that the strength of the
perturbation cannot be well controlled. We firstly provide a perturbation
framework on graphs by introducing weights on the nodes, of which the magnitude
of perturbation can be easily controlled through the variance of the weights.
Meanwhile, the topology of the graphs are also preserved to avoid
uncontrollable strength in the perturbation. We then extend the measure of
robustness in the robust statistics literature to the graph properties.

36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an