  Graph Laplacian (GL)-based semi-supervised learning is one of the most used
approaches for classifying nodes in a graph. Understanding and certifying the
adversarial robustness of machine learning (ML) algorithms has attracted large
amounts of attention from different research communities due to its crucial
importance in many security-critical applied domains. There is great interest
in the theoretical certification of adversarial robustness for popular ML
algorithms. In this paper, we provide the first adversarial robust
certification for the GL classifier. More precisely we quantitatively bound the
difference in the classification accuracy of the GL classifier before and after
an adversarial attack. Numerically, we validate our theoretical certification
results and show that leveraging existing adversarial defenses for the
$k$-nearest neighbor classifier can remarkably improve the robustness of the GL
classifier.
