  Graph Neural Networks (GNNs) as deep learning models working on
graph-structure data have achieved advanced performance in many works. However,
it has been proved repeatedly that, not all edges in a graph are necessary for
the training of machine learning models. In other words, some of the
connections between nodes may bring redundant or even misleading information to
downstream tasks. In this paper, we try to provide a method to drop edges in
order to purify the graph data from a new perspective. Specifically, it is a
framework to purify graphs with the least loss of information, under which the
core problems are how to better evaluate the edges and how to delete the
relatively redundant edges with the least loss of information. To address the
above two problems, we propose several measurements for the evaluation and
different judges and filters for the edge deletion. We also introduce a
residual-iteration strategy and a surrogate model for measurements requiring
unknown information. The experimental results show that our proposed
measurements for KL divergence with constraints to maintain the connectivity of
the graph and delete edges in an iterative way can find out the most edges
while keeping the performance of GNNs. What's more, further experiments show
that this method also achieves the best defense performance against adversarial
attacks.
