  Graph convolutional networks (GCNs) are vulnerable to perturbations of the
graph structure that are either random, or, adversarially designed. The
perturbed links modify the graph neighborhoods, which critically affects the
performance of GCNs in semi-supervised learning (SSL) tasks. Aiming at
robustifying GCNs conditioned on the perturbed graph, the present paper
generates multiple auxiliary graphs, each having its binary 0-1 edge weights
flip values with probabilities designed to enhance robustness. The resultant
edge-dithered auxiliary graphs are leveraged by an adaptive (A)GCN that
performs SSL. Robustness is enabled through learnable graph-combining weights
along with suitable regularizers. Relative to GCN, the novel AGCN achieves
markedly improved performance in tests with noisy inputs, graph perturbations,
and state-of-the-art adversarial attacks. Further experiments with protein
interaction networks showcase the competitive performance of AGCN for SSL over
multiple graphs.
