Leaders in communities of real-world networks

Community structures have important influence on the properties and dynamic characteristics of the complex networks. However, to the best of our knowledge, there is not much attention given to investigating the internal structure of communities in the literature. In this paper, we study community structures of more than twenty existing networks using ten commonly used community-detecting methods, and discovery that most communities have several leaders whose degrees are particularly large. We use statistical parameter, variance, to classify the communities as leader communities and self-organized communities. In a leader community, we defined the nodes with largest 10% degree as its leaders. In our experiences, when removing the leaders, on average community's internal edges are reduced by more than 40% and inter-communities edges are reduced by more than 20%. In addition, community's average clustering coefficient decreases. These facts suggest that the leaders play an important role in keeping communities denser and more clustered, and it is the leaders that are more likely to link to other communities. Moreover, similar results for several random networks are obtained, and a theoretical lower bound of the lost internal edges is given. Our study shed the light on the further understanding and application of the internal community structure in complex networks.