Network service, as a behavioral process oriented toward network operation, plays a vital role in the function of network application system. State-of-the-art researches are prone to ignore the intrinsic behavioral characteristics of network services, and yield subjective and biased analysis results on service selection, coordination, composition, and management. To fill in this gap, an approach of calculating the network service behavioral utility is presented in this paper. We first propose a method of extracting the behavioral attributes and constructing the state space model of network service with machine learning and differential geometry techniques. Moreover, based on the state space model, which is described as Riemannian manifold, we propose a method of calculating the utility of network services and applications, which serves as a measure of impact of the particular network behavior. The proposed method is examined in different application scenarios under the service mesh architecture, and experimental results show that the method can effectively reflect the intrinsic behavioral characteristic of network service.