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Sender--Receiver Community Detection in Directed Networks...
Duy Hieu Do · 2026-06-16 · via cs.SI updates on arXiv.org

Directed community detection is challenging because edge directions encode asymmetric source-target relations. Most directed modularity and random-walk methods assign one label to each vertex, whereas recent bimodularity-based methods cluster directed edges more freely. We propose TT-SR, a Two-Tier Sender-Receiver framework that lies between these two viewpoints. Each vertex is assigned a sender role and a receiver role, and each directed edge receives the type induced by the sender role of its source and the receiver role of its target. Thus, TT-SR is more expressive than one-label vertex clustering while remaining more interpretable than unrestricted edge clustering. The method generates candidate sender-receiver assignments from count-residual, stationary-flow, degree-corrected, and order-score views. The candidates are refined by local role updates and selected by a two-tier rule: a degree-corrected profile score provides the primary structural criterion, while Bernoulli density and order-flow scores are used only as secondary ranking signals. We justify the main spectral views through sender-receiver modularity relaxations and interpret the degree-corrected score as a likelihood-based residual comparison. Experiments on pathway-type, co-block, and ordered-flow synthetic benchmarks show that TT-SR achieves the strongest or essentially tied strongest edge-community recovery across three scale settings. The gains are most pronounced on degree-corrected co-block and ordered-flow graphs. Real-network diagnostics further indicate that TT-SR aligns well with Email-Eu-core metadata and extracts strong sender-receiverbicommunity summaries on unlabeled directed networks.