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, this study explores a repetition coding scheme with sender-assigned noise and majority voting on the receiver's end to rectify the graph's structure. The approach operates without prior knowledge of the attack's characteristics. We analytically derive a bound on the number of repetitions needed to satisfy probabilistic constraints on the quality of the reconstructed graph. The method can accurately and effectively decode Erdős-Rényi graphs that were subjected to nonrandom edge removal, namely, those connected to vertices with the highest eigenvector centrality, in addition to random addition and removal of edges by the attacker. The method is also effective against attacks on large scale-free graphs generated using the Barabási-Albert model but require a larger number of repetitions than needed to correct Erdős-Rényi graphs.