Optimal Selection of Informed Agents for Influence Opposition

There is no doubt that the members of a society can influence each other and a minority of them may guide, in some situations, the whole society toward a particular opinion. However, the promoted opinion is not always desirable, and in some cases, it is desired to prevent its propagation in the network. This mission can be done with the help of informed agents that are common agents that act as hidden advertisers. In this article, we will discuss how many and which agents should be selected as informed agents in a way that the final opinions of agents satisfy some given constraints. In the line of solving this problem, the notion of equilibratability is considered, and the problem is formulated as minimizing the zero-norm of available solutions. Knowing that the mentioned problem is NP-hard, some relaxation methods are considered to solve this problem. The efficiency of the proposed methods is investigated for selecting the sparsest solution in a well-known graph. Finally, the required informed agents to resist a group of spreaders in some random graphs [generated with different methods, such as Erdös and Rényi (ER), Watts and Strogatz (WS), and Barabási and Albert (BA)] are compared, and some reasonable results are observed.