At the beginning of social networks, the number of users was lower than in the present period. Over time, social networks have evolved. Today, social networks have become one of the main factors of communication in the world. As the number of users, thus the data increased, it was decided that it is necessary to conduct an analysis of data that could be used more effectively. This was the main reason for development of analysis of social networks. This paper studies the detection of community social networks. Detection of community social networks are used to benefit the user preferences and thus grouping users in simple clusters, that could be easier to analyze. Detection is based on clustering, which can be hierarchical and based on the means. The most famous is the k-means algorithm, which is analyzed in this paper with the actual data from the social network Facebook by using the statistics tool R. Software environment Gephi and Rstudio has also been used, which primarily serves to analyze a large number of data and their visualization. Visualization of the algorithm is proven the usefulness of the implementation of the detection of community social networks in reality, and thus opened up the possibility of optimizing existing algorithms. Detection of community social networks can greatly help in analyzing a large number of users, so that social networks could more easily adapt to users. This fact alone means that in the future social networks will be developed in the high-quality network and that the credit for this success will be exact same branch of mathematics - analysis of social networks.