Forward--Backward Green Cosine Geometry for Directed Community Detection and Overlap Expansion

Duy Hieu Do's paper, 'Forward--Backward Green Cosine Geometry for Directed Community Detection and Overlap Expansion,' tackles the challenges of community detection in directed graphs. Traditional methods struggle due to edge asymmetry, which complicates the diffusion of information. Do's innovative approach utilizes Green-based cosine geometry to refine hitting-time data, creating a more effective model for clustering. By replacing raw hitting-time vectors with centered Green profiles, the algorithm can better account for directionality in graphs.

The framework introduces two algorithms: Di-Green-FB-cosine-KMeans for creating disjoint directed partitions and Di-Green-FB-Cosine Overlap for expanding these partitions into overlapping covers. Initial experiments, conducted on synthetic benchmarks, demonstrate that this new geometry outperforms conventional hitting-time cosine variants and competes well with spectral and flow-based methods. Moreover, real-network evaluations show that the geometry yields coherent directed partitions, providing a significant advancement in the field of social and information networks. The method's ability to recover additional memberships in moderately and weakly separated directed networks further underscores its potential applications in complex community detection scenarios.