The diffusion of charged particles in a graph can be modeled using random walks on a weighted graph. We give strategies to hide (or cloak) changes in a subgraph from the perspective of measurements of expected net particle charges made at nodes away from the cloaked subgraph. We distinguish between passive and active strategies, depending on whether the strategy involves injecting particles. The passive strategy can hide topology and edge weight changes. In addition to these capabilities, the active strategy can also hide sources of particles, at the cost of prior knowledge of the expected net particle charges in the reference graph. The strategies we present rely on discrete analogues of classic potential theory, that include a Calder\'on calculus on graphs.

翻译：带电粒子在图中的扩散可以用加权图上的随机游走来建模。我们提出策略以隐藏子图的变化，使其不被在远离隐身子图的节点上对预期净粒子电荷的测量所察觉。根据是否涉及注入粒子的策略，我们区分了被动和主动策略。被动策略可以隐藏拓扑结构和边权重的变化。除上述能力外，主动策略还能隐藏粒子源，但代价是需要事先了解参考图中预期净粒子电荷的先验知识。我们提出的策略依赖于经典势理论的离散类比，包括图上的Calderón微积分。