Scalable Spectral Algorithms for Community Detection in Directed Networks

Community detection has been one of the central problems in network studies and directed network is particular challenging due to asymmetry among its links. In this paper, we found that incorporating the direction of links reveals new perspective on communities regarding to two different roles, source and terminal, that a node plays in each community. Intriguingly, such communities appear to be connected with unique spectral property of the graph Laplacian of the adjacency matrix and we exploit this connection by using regularized SVD methods. We propose harvesting algorithms, coupled with regularized SVDs, that are linearly scalable for efficient identification of communities in huge directed networks. The algorithm showed great performance and scalability on benchmark networks in simulations and successfully recovered communities in real networks applications (with ~ 2 million nodes and ~ 50 million edges).