On countering adversarial perturbations in graphs using error correcting codes

We consider the problem of a graph subjected to adversarial perturbations, such as those arising from cyber-attacks, where edges are covertly added or removed. The adversarial perturbations occur during the transmission of the graph between a sender and a receiver. To counteract potential perturbations, we explore a repetition coding scheme with sender-assigned binary noise and majority voting on the receiver's end to rectify the graph's structure. Our approach operates without prior knowledge of the attack's characteristics. We provide an analytical derivation of a bound on the number of repetitions needed to satisfy probabilistic constraints on the quality of the reconstructed graph. We show that the method can accurately decode graphs that were subjected to non-random edge removal, namely, those connected to vertices with the highest eigenvector centrality, in addition to random addition and removal of edges by the attacker.