A framework of mapping undirected to directed graphs for community detection

Community detection gives us a new way to understand the organization characteristics of complex systems. However, for simplicity, most methods for community detection always model the systems as an undirected graph. In this paper, we propose a new framework that unifies undirected into directed graphs by a function, which creates a mapping that transforms an undirected graph into its two directed modes for community detection. We take the method of modularity optimization as an example and apply it on our framework to uncover community structure in complex networks. Compared with the original modularity optimization, we find that the modularity optimization on our framework not only achieves better results on the LFR benchmark, but also a more detailed subdivision on the Zachary club network and the American college football network. Based on the results above, we confirm that our framework provides a good platform for community detection.