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.

翻译：本文研究了遭受对抗性扰动的图结构问题，此类扰动通常源于网络攻击，表现为对图中边的隐蔽增删操作。对抗扰动发生在图结构从发送方向接收方传输的过程中。为抵御潜在扰动，我们探索了一种采用发送端分配二进制噪声的重复编码方案，并在接收端通过多数表决机制校正图结构。该方法无需预先获知攻击特征。我们通过理论分析推导了满足重构图质量概率约束所需重复次数的上界。研究表明，该方法能够准确解码遭受非随机边删除（即针对最高特征向量中心性顶点的连接边）以及攻击者随机增删边的图结构。