Title: Measuring the Robustness of Graph Properties,
Abstract: 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.