Community detection in networks: The leader-follower algorithm

Traditional spectral clustering methods cannot naturally learn the number of communities in a network and often fail to detect smaller community structure in dense networks because they are based upon external community connectivity properties such as graph cuts. We propose an algorithm for detecting community structure in networks called the leader-follower algorithm which is based upon the natural internal structure expected of communities in social networks. The algorithm uses the notion of network centrality in a novel manner to differentiate leaders (nodes which connect different communities) from loyal followers (nodes which only have neighbors within a single community). Using this approach, it is able to naturally learn the communities from the network structure and does not require the number of communities as an input, in contrast to other common methods such as spectral clustering. We prove that it will detect all of the com-munities exactly for any network possessing communities with the natural inter-nal structure expected in social networks. More importantly, we demonstrate the effectiveness of the leader-follower algorithm in the context of various real net-works ranging from social networks such as Facebook to biological networks such as an fMRI based human brain network. We find that the leader-follower algo-rithm finds the relevant community structure in these networks without knowing the number of communities beforehand. Also, because the leader-follower algo-rithm detects communities using their internal structure, we find that it can resolve a finer community structure in dense networks than common spectral clustering methods based on external community structure.