This article provides a novel and practical approach for investigating the characteristics of intercity telecommunication network whose overall and complete information is unavailable. Using a mobile phone call data set covering 4.39 million subscribers registered in a particular region, we construct two intercity mobile communication subnets and infer characteristics of the whole intercity mobile communication network of China. Results confirm that intercity communication intensity is characterized by the gravity model. The communication intensity based on mobile call number decreases along the distance with a scaling exponent 0.5, whereas the scaling exponent for the communication intensity based on mobile call duration is 0.4. Moreover, we uncover the rank-size distribution of tie strength (mobile call number and duration) between a city and its neighbours. The rank-size law of tie strengths between cities is mainly determined by the rank-size distribution of cities. The distance between cities plays a less decisive role than the size distribution in the network, but significantly impacts mobile communication patterns. The call duration of individual intercity mobile communication is generally positively correlated to the communication distance, explaining why the distance decay of communication intensity based on call durations is slower than that based on call numbers. The contribution of this research is twofold. First, we identify the distance decay effect in intercity mobile communications of China and uncover the dominant impact of the rank-size distribution of cities. Second, a method for estimating the properties of the whole network according to the observed interactions of its subnets is developed.