Extracting hierarchies with overlapping structure from network data

Relationships between entities in many complex systems, such as the Internet and social networks, have a natural hierarchical organization. Understanding these inherent hierarchies is essential for creating models of these systems. Thus, there is a recent body of research concerning the extraction of hierarchies from networks. We propose a new method for modeling hierarchies through extracting the affiliations of the network. From these affiliations, we construct a lattice of the relationships between nodes. A principal advantage of our approach is that any overlapping community structures of the nodes within the network have a natural representation within the lattice. We then show an example of our method using a real data set.