arXiv subjects

Duy Hieu Do

Publications and source records attributed to Duy Hieu Do.

3 recordsLinked to original sources

arXiv2026

Sender--Receiver Community Detection in Directed Networks via Node-Role-Constrained Edge Clustering

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.

cs.SI↗

arXiv2026

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

Community detection in directed graphs is challenging because edge asymmetry induces non-reversible diffusion, direction-dependent accessibility, and distinct source and target roles. This paper develops a Green-based cosine geometry for directed community detection and for expanding a disjoint partition into an overlapping cover. The key observation is that hitting-time information is natural for directed graphs, but raw hitting-time vectors are not well suited for cosine comparison: they contain a source-independent stationary baseline, whereas cosine similarity is not translation-invariant. We therefore replace raw hitting-time profiles by centered Green profiles of the directed random walk and use the diffusive part of the truncated Green profile, excluding the time-zero self-spike. To account for asymmetry, we concatenate the Green profile of the original walk with the corresponding profile on the edge-reversed graph, yielding forward--backward Green coordinates. The framework gives two algorithms. Di-Green-FB-cosine-KMeans clusters vertices in the Green cosine space to obtain a disjoint directed partition. Di-Green-FB-Cosine Overlap expands an initial partition into an overlapping cover using a community-adaptive cosine rule. The initial partition can be supplied by any disjoint method; in the main pipeline it is produced by Di-Green-FB-cosine-KMeans. Experiments on synthetic directed benchmarks show that the proposed geometry improves over raw hitting-time cosine variants and is competitive with directed spectral and flow-based baselines. Real-network experiments, evaluated by directed modularity as an internal quality measure, indicate that the same geometry produces coherent directed partitions. Synthetic overlap experiments further show that the method recovers additional memberships effectively, especially in moderately and weakly separated directed networks.

cs.SI↗

arXiv2024

An improvement on the Louvain algorithm using random walks

We will present improvements to famous algorithms for community detection, namely Newman's spectral method algorithm and the Louvain algorithm. The Newman algorithm begins by treating the original graph as a single cluster, then repeats the process to split each cluster into two, based on the signs of the eigenvector corresponding to the secondlargest eigenvalue. Our improvement involves replacing the time-consuming computation of eigenvalues with a random walk during the splitting process. The Louvain algorithm iteratively performs the following steps until no increase in modularity can be achieved anymore: each step consists of two phases, phase 1 for partitioning the graph into clusters, and phase 2 for constructing a new graph where each vertex represents one cluster obtained from phase 1. We propose an improvement to this algorithm by adding our random walk algorithm as an additional phase for refining clusters obtained from phase 1. It maintains a complexity comparable to the Louvain algorithm while exhibiting superior efficiency. To validate the robustness and effectiveness of our proposed algorithms, we conducted experiments using randomly generated graphs and real-world data.

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