Social network analysis with large volumes of data and complex communication structures is so difficult and time-consuming. Community detection is one of the major challenges in network analysis. A community is a set of individuals or organizations whose communication density is more than other network entities. Community detection or clustering can reveal the structure of groups in social networks, or relationships between entities. The label Propagation Algorithms with neighbor node influence have less complexity than traditional Algorithms, such as clustering, to recognize communities. Also, the Algorithms can identify overlapping communities. In our label Propagation Algorithm, which is based on the neighbor node influence, important nodes are more likely to publish their labels, while less important nodes have a small chance of spreading the label. The degree of similarity of nodes and the effect of nodes in a social network depends on the parameter of path length between nodes. In the proposed method, increasing this parameter leads to more accurate identification of overlapping and stable communities. The proposed Algorithm detects overlapping communities with the same accuracy as the previous Algorithms with fewer iterations, in less time. The Algorithm is implemented on real and artificial social networks with weightless graphs and weighted graphs with weighting by Jacquard similarity criterion, in all of which the execution time is improved.