Recursive Clustering Methods for Network Analysis

We study axiomatically recursive clustering methods for networks. Such methods can be used to identify community structures of a network. One of the methods is based on identifying a node subset that maximizes the average degree within this subset. Once such a subset is found, the method is applied on the subnetwork whose node set is the complement of the first cluster, and so on recursively. The method produces an ordered partition of the node set of the original network. We give a list of axioms that this method satisfies, and show that any recursive clustering method satisfying the same set of axioms must produce the same or a coarser partition than our method.