Due to the effective role that social networks play in daily life, the analysis of social networks has attracted lots of attention in recent twenty years. There are several key problems related to identifying so-called influential users for several applications, which need to spread messages. These problems are studied by researchers from different perspectives. Among them, the approaches used to estimate users’ influence are important and generally can be reflected by problems’ objective functions. For a problem, the property of its objective function is a top of interest as it may influence the method used to solving this problem. In related research, when the objective function of the studied problem is defined, the analysis about its submodularity is introduced and followed by the details of algorithm proposed to address the problem and related to the result of analysis. As a result, recent years have witnessed the increasing importance of submodular and nonsubmodular optimization in study of social networks, and there are obvious mutual promoting effects between them.