Countering adversarial perturbations in graphs using error correcting codes

TL;DR

This paper introduces a coding-based method to detect and correct adversarial modifications in graphs, such as added or removed edges, without prior attack knowledge, ensuring reliable graph transmission.

Contribution

It proposes a repetition coding scheme with majority voting to counteract adversarial graph perturbations, providing analytical bounds and demonstrating effectiveness on various graph models.

Findings

Effective decoding of Erdős-Rényi graphs under attack

Successful correction of targeted edge removals based on eigenvector centrality

Applicable to large-scale scale-free graphs with increased repetitions

Abstract

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 Erd\H{o}s-R\'{e}nyi 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. The method is also effective against attacks on large scale-free graphs generated using the Barab\'{a}si-Albert model but require a larger number of repetitions than needed to correct Erd\H{o}s-R\'{e}nyi graphs.