In recent years, epidemic processes (e.g., virus dissemination and information) on networks have garnered considerable social attention. Understanding the characteristics of epidemic processes and developing methods to suppress or promote these epidemic processes effectively are critical challenges in modern society. In a previous study, epidemic processes on networks are modeled using adjacency matrices, revealing that the largest eigenvalue of the adjacency matrix strongly influences the expansion of a diffusion on the network. Based on the revealed knowledge, the methods have been proposed to manipulate the largest eigenvalue of the adjacency matrix. In the methods, deletion or addition links are selected based on matrix perturbation theory so that the largest eigenvalue can be effectively decreased or increased. However, this link selection works well only when the spectral gap (the difference between the largest and the second largest eigenvalue) is sufficiently large. In general, real world networks possess a cluster structure, and networks with a stronger cluster structure tend to have smaller spectral gaps. Therefore, in order to apply the eigenvalue manipulation for practical diffusion suppression or promotion, it is desirable to understand how cluster structures influence its effectiveness. Accordingly, in this paper, we elucidate the impact of cluster structure on the effectiveness of the eigenvalue manipulation through evaluations that use various networks with cluster structures.