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Community detection is crucial for analyzing the structure of social networks and extracting hidden information from them. The goal is to find groups of nodes (communities) with high intra-group and low inter-group communications. This problem is NP-hard, and most existing algorithms are global with high computational complexity, especially for large networks. Recently, local methods with acceptable computational complexity have been developed, but many have low accuracy and are non-deterministic. This paper introduces a new local algorithm, LCD-SN, which identifies communities based on first- and second-degree neighbor nodes. Unlike other local algorithms, LCD-SN is highly accurate, definitive, and not dependent on initial seed nodes. Additionally, a new index is proposed to determine the importance of network nodes using their local characteristics (first- and second-degree neighbors). Using this index, LCD-SN first identifies important nodes, forms initial communities with these nodes and their first-degree neighbors, and then obtains final communities through post-processing. Experiments show that LCD-SN is effective in identifying communities in social networks.