Nowadays, social networks have been widely used by different people for different purposes in the world. The discovering of communities is a widespread subject in the space of social networks analysis. Many interesting solutions have been proposed in the literature. However, most solutions have common problems: the stability and the community structures quality. In this paper, we propose a new model to find communities based on a new concept called 'large families'. This model will be used, to motivate a community detection strategy to identify and effectively monitor the evolution of dynamic communities. We propose a compromise between the stability and the quality metrics. We apply our model on a real social network of the karate club of Zachary. Also, we describe experiences of our model on a large scale network of Enron's email data set as broader Benchmark Network. Simulations results show that our proposed model is globally satisfactory.