Community or module structure is a natural property of complex networks. Leader communities and self-organizing communities have been introduced recently to characterize networks and understand how communities arise in complex networks. However, identification of leader and self-organizing communities is technically challenging since no adequate quantification has been developed to properly separate the two types of communities. We introduced a new measure, called ratio of node degree variances, to distinguish leader communities from self-organizing communities, and developed a statistical model to quantitatively characterize the two types of communities. We experimentally studied the power and robustness of the new method on several real-world networks in combination of some of the existing community identification methods. Our results revealed that social networks and citation networks contain more leader communities whereas technological networks such as power grid network have more self-organizing communities. Moreover, our results also indicated that self-organizing communities tend to be smaller than leader communities. The results shed new lights on community formation and module structures in complex systems.