Since the environment around us is changing continuously, we need to use special models to describe such dynamic processes. Evolutionary games is the section of the game theory, which provides a wide range of tools for formalization the adaptation process of agents to the environment. In this current work we consider an evolution game which takes into account a structure of population. Here the structure of population is define by different types or graphs such as ring or greed. Hence the network is a way to establish a connection between the agents of a population. The structure influences the process of evolution and resulting states of population and we can show that the structure of the networks restricts the regular evolutionary process. The paper describes the evolution process taking into account various network structures.