Community detection has gained much attention during the past few decades. So many algorithms have been developed to tackle this problem. In previous related works the weight of the edges and directionality were not considered at the same time in the models. Considering weights and directionality makes the models more realistic and prevents the loss of information in the network. In this article, we propose an overlapping community detection algorithm for networks with weighted and directed edges. We used the concept of information flows among the vertices i.e. the more flows exist in a community, the stronger the community. We implemented the concept of flow using weighted closed flows starting from a given node and ending to the same node. By using the mentioned assumption we developed a new modularity measure called weighted flow modularity (WFM) based on M function modularity. In addition, we developed an overlapping score criteria which considers overlap in vertices and edges at the same time and is much faster in the terms of run time. We compared the community detection results in terms of accuracy and running time with Order statistics local optimization method (OSLOM) on 74 LFR benchmark networks using normalized mutual information score. We also implemented the community detection process using LCFE on real world datasets and evaluated the community detection results using EQ measure. The experimental analysis results show that the LCFE is more accurate in most cases and is competitive in other cases with OSLOM.