The central community of social networks, usually represented through the highest degree k-core of the corresponding graph, is proposed here as a compact representation of large social networks. We show that the central community of egocentric social media networks, such as the ego networks on Twitter and Instagram, tell us much more about the actual influence of the ego than the whole egocentric network itself. We also propose a novel genetic algorithm for the identification of central community of egocentric social networks and we examine the importance of the proper initialisation of this algorithm. The actual Twitter ego networks we used in our experiments along with the corresponding Python code are made publicly available for anyone who wishes to use them.