Non-assortative Community Structures in Complex Networks

Abstract

The identification of mesoscale structures is essential to understand the organization of complex networks. Despite the recognition of various structural patterns in many networks, previous works on the detection of groups of users have focused on finding specific types, such as assortative and core-periphery structures, and developing computational methods to find these mesoscale structures within a network. In this project, we go beyond the problem of detecting a specific type of mesoscale arrangement and instead ask what type of mesoscale structures exist, how typical each is, and how we can interpret them. We develop a methodology to systematically classify community structures in directed multi-graphs based on pairwise group relationships. One novel structure, termed a "source-basin," reveals unique information flow from sparsely to densely connected nodes. We also introduce a generative network model that reproduces four community types, finding that differences in average in-degree are key for source-basin formation. Our methods are applied to social media data to examine the role of community structures in real networks.