  Graph-structured data is ubiquitous in practice and often processed using
graph neural networks (GNNs). With the adoption of recent laws ensuring the
``right to be forgotten'', the problem of graph data removal has become of
significant importance. To address the problem, we introduce the first known
framework for \emph{certified graph unlearning} of GNNs. In contrast to
standard machine unlearning, new analytical and heuristic unlearning challenges
arise when dealing with complex graph data. First, three different types of
unlearning requests need to be considered, including node feature, edge and
node unlearning. Second, to establish provable performance guarantees, one
needs to address challenges associated with feature mixing during propagation.
The underlying analysis is illustrated on the example of simple graph
convolutions (SGC) and their generalized PageRank (GPR) extensions, thereby
laying the theoretical foundation for certified unlearning of GNNs. Our
empirical studies on six benchmark datasets demonstrate excellent
performance-complexity trade-offs when compared to complete retraining methods
and approaches that do not leverage graph information. For example, when
unlearning $20\%$ of the nodes on the Cora dataset, our approach suffers only a
$0.1\%$ loss in test accuracy while offering a $4$-fold speed-up compared to
complete retraining. Our scheme also outperforms unlearning methods that do not
leverage graph information with a $12\%$ increase in test accuracy for a
comparable time complexity.
