  Graph Neural Networks (GNNs) have demonstrated state-of-the-art performance
in various graph representation learning tasks. Recently, studies revealed
their vulnerability to adversarial attacks. In this work, we theoretically
define the concept of expected robustness in the context of attributed graphs
and relate it to the classical definition of adversarial robustness in the
graph representation learning literature. Our definition allows us to derive an
upper bound of the expected robustness of Graph Convolutional Networks (GCNs)
and Graph Isomorphism Networks subject to node feature attacks. Building on
these findings, we connect the expected robustness of GNNs to the
orthonormality of their weight matrices and consequently propose an
attack-independent, more robust variant of the GCN, called the Graph
Convolutional Orthonormal Robust Networks (GCORNs). We further introduce a
probabilistic method to estimate the expected robustness, which allows us to
evaluate the effectiveness of GCORN on several real-world datasets.
Experimental experiments showed that GCORN outperforms available defense
methods. Our code is publicly available at:
\href{https://github.com/Sennadir/GCORN}{https://github.com/Sennadir/GCORN}.
