Ridesharing services play an essential role in modern transportation, which significantly reduces traffic congestion and exhaust pollution. In the ridesharing problem, improving the sharing rate between riders can not only save the travel cost of drivers but also utilize vehicle resources more efficiently. The existing online-based and batch-based methods for the ridesharing problem lack the analysis of the sharing relationship among riders, leading to a compromise between efficiency and accuracy. In addition, the graph is a powerful tool to analyze the structure information between nodes. Therefore, in this paper, we propose a framework, namely StructRide, to utilize the structure information to improve the results for ridesharing problems. Specifically, we extract the sharing relationships between riders to construct a shareability graph. Then, we define a novel measurement shareability loss for vehicles to select groups of requests such that the unselected requests still have high probabilities of sharing. Our SARD algorithm can efficiently solve dynamic ridesharing problems to achieve dramatically improved results. Through extensive experiments, we demonstrate the efficiency and effectiveness of our SARD algorithm on two real datasets. Our SARD can run up to 72.68 times faster and serve up to 50% more requests than the state-of-the-art algorithms.