Natural networks such as those between humans observed through their interactions or biological networks predicted based on various experimental measurements contain a wealth of information about the unobserved structure of the social or biological system. However, these networks are inherently noisy in the sense that they contain spurious connections making them seemingly dense. Therefore, identifying important, refined structures such as communities or clusters becomes quite challenging. Specifically, we find that the popular, traditional method of spectral clustering does not manage to learn refined community structure. The primary reason for this is that it is based upon external community connectivity properties such as graph-cuts. Motivated to overcome this limitation, we propose a community detection algorithm, called the leader-follower algorithm, based upon identifying the natural internal structure of the expected communities. The algorithm uses the notion of network central...