SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2321-2345, January 2021.
This paper considers a social network modeled as an Erdös--Rényi random graph. Each individual in the network updates her opinion using the weighted average of the opinions of her neighbors. We explore how an external manipulative agent can drive the opinions of these individuals to a desired state with a limited additive influence on their innate opinions. We show that the manipulative agent can steer the network opinion to any arbitrary value in finite time (i.e., the system is controllable) almost surely when there is no restriction on her influence. However, when the control input is sparsity constrained, the network opinion is controllable with some probability. We lower bound this probability using the concentration properties of random vectors based on the Lévy concentration function and small ball probabilities. Our theoretical and numerical results shed light on how controllability of the network opinion depends on the parameters such as the size and the connectivity of the network and sity constraints faced by the manipulative agent.

中文翻译：

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Erdös网络观点的可控性--Rényi图使用稀疏控制输入

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2321-2345 页，2021 年 1 月。
本文考虑建模为 Erdös--Rényi 随机图的社交网络。网络中的每个人都使用邻居意见的加权平均值来更新自己的意见。我们探索外部操纵代理如何将这些人的意见驱动到理想状态，而对其先天意见的附加影响有限。我们表明，当对她的影响没有限制时，操纵代理几乎可以肯定地将网络意见引导到有限时间内的任意值（即系统是可控的）。然而，当控制输入是稀疏约束时，网络意见是可控的，有一定的概率。我们使用基于 Lévy 集中函数和小球概率的随机向量的集中属性来降低这个概率。