With the development of the Internet of Things and smart cities, edge computing has gradually become a key technology for real-time data processing. The traditional cloud computing model has obvious limitations in data transmission and processing delay. This paper proposes a concurrent graph data sharing and resource optimization model, which aims to improve the resource utilization and computing efficiency of edge computing nodes in the process of concurrent execution of multi-tasks. By analyzing the data access pattern of tasks, the Longest Common Subsequence (LCS) algorithm was used to optimize the data sharing strategy, and the data read sequence was dynamically adjusted to reduce data transmission and repeated calculation. The experimental results show that the proposed model is superior to the traditional method in terms of task execution time, data transmission volume and resource utilization. The task execution time is shortened by about 33.3%, the data transmission volume is reduced by about 46%, and the resource utilization rate is improved by about 20%. This research provides an efficient solution for real-time data processing in edge computing environments, which holds significant importance for fields such as the Internet of Things (IoT), industrial automation, and smart cities.