Identifying overlapping communities is a fundamental but non-trivial aspect of network analysis, particularly in large-scale complex networks. This task becomes even more difficult when addressing attributed weighted networks, such as social media platforms (e.g. Facebook, X, and LinkedIn), biological systems, and neural networks. To address this, we developed a seed expansion-based algorithm named DOC-WAN, which stands for Detection of Overlapping Communities in Weighted Attributed Networks. The algorithm starts by selecting a seed node based on weighted centrality and then expand it using both Hamming similarity and neighbourhood proximity to form an initial community. This process is repeated as long as there are unassigned nodes. Finally, highly similar communities are merged to produce the overlapping community structure. DOC-WAN was rigorously evaluated on 10 real-world attributed networks, spanning from sparse to dense structures and exhibiting significant variation in size and structural properties. To assess its effectiveness and stability, the algorithm was evaluated using four quality measures and four stability metrics, along with their average scores. Results demonstrated that DOC-WAN consistently achieved high-quality scores and exceptional stability across almost all networks, underscoring its robustness and adaptability. The algorithm’s time complexity is 𝒪(nc_max (k_max^2 + ℓ )) , where n represents the number of nodes, ℓ represents the dimension of attributes, k_max is the maximum degree of nodes, and c_max is the maximum number of initial communities. Through systematic experimentation, we demonstrate that DOC-WAN effectively detects overlapping communities in attributed weighted networks. The framework yields high-quality community structures and stable performance, offering a viable approach for complex network analysis. However, a key limitation of the current framework lies in its parameterization; although the default parameters provided the best results in this study, tuning them for diverse datasets remains challenging. Therefore, developing automated, self-tuning selection mechanisms is highly recommended for future work.
Graph contrastive learning (GCL) learns representations from augmented graph views, whose topology perturbations can distort node-level degree information. We characterize this distortion through marginal structural distributions (MSDs), the normalized row and column sums of a weighted adjacency matrix. We propose OTGCL, which combines Diverse Optimal Transport Augmentation (DOTA) with Marginal Structure-based Sampling (MSS). DOTA constructs topological views through local optimal transport under constraints that preserve each node’s incoming and outgoing weighted degrees. Random subgraph sampling provides diverse views and limits the transport problem size; MSS uses degree information to select within-view negatives. Experiments on eight benchmark graphs show gains in degree prediction and competitive results on node classification and link prediction, together with benefits from using DOTA in the tested GCL backbones. Structural measurements verify weighted-marginal preservation to numerical precision and quantify changes in binary degrees and higher-order properties. Cost and sampling studies reveal graph- and task-dependent responses. Local optimal transport also supports representation learning on larger graphs. Together with computational measurements, these studies characterize the predictive performance and cost of weighted-marginal-preserving augmentation.
Heterogeneous graph neural networks (HGNNs) play a crucial role in modeling complex real-world data with multiple node and edge types. However, existing methods, including both metapath-based and metapath-free methods, struggle to balance the capture of local semantic structures with the modeling of long-range semantic associations. To address this problem, we propose HGMamba, a dual-path heterogeneous graph neural network equipped with a selective state space model, namely Mamba. HGMamba is motivated by the observation that long-range dependency in heterogeneous graphs is a two-level semantic problem. Specifically, it involves graph-distance dependency within metapath tokens and cross-semantic dependency across metapath tokens. To capture both levels of dependency, we propose a metapath-guided selective state space module. This module compresses the multi-hop neighborhood of each metapath into a semantic token and applies Mamba to model the joint semantics across tokens in linear time, thereby covering both levels of long-range dependency. The resulting sequence is constructed from metapath-level tokens rather than serialized nodes, which preserves the type-specific semantic structure of heterogeneous graphs. In this way, the module serves as the long-range path of HGMamba. In parallel, an attention-based local path employs type-specific feature projections and multi-head attention to encode fine-grained neighborhood semantics. Finally, an adaptive gating mechanism dynamically fuses the complementary representations of the two paths, effectively balancing semantic information across different ranges. Extensive experiments on four benchmark datasets indicate that HGMamba significantly outperforms state-of-the-art HGNNs on the vast majority of evaluation metrics and tasks. These results validate its effectiveness in integrating multi-scale semantic information.
Markov clustering (MCL) is a widely used clustering algorithm for graph data partitioning. However, it suffers from three key limitations: the lack of theoretical investigation into the reliability of graph construction methods for MCL, difficulty in parameter expansion tuning, and the reliance on global pruning strategies that ignore local structural variations. To address these issues, we propose enhanced Markov clustering (EMC), which introduces three innovations: (1) A theoretically supported RkNN-based graph construction, which we demonstrate to be consistent with MCL’s inflow, thereby providing a principled basis for identifying natural cluster centers; (2) A minimal-but-maximal expansion strategy that adaptively determines the optimal expansion power, preventing over-merging and fragmentation; and (3) Local adaptive pruning, a column-wise pruning mechanism that removes weak inter-cluster edges more effectively than global pruning while preserving local structure. Experiments on benchmark datasets show that EMC generally outperforms existing MCL variants and is competitive with other effective clustering algorithms on tabular data while reducing hyperparameter tuning complexity.
Semantic web service discovery faces scalability challenges associated with increasing repository size, heterogeneous ontology structures, and the computational overhead of semantic matching and ranking. This work presents a clustering-assisted knowledge graph embedding (KGE) framework for semantic web service discovery and recommendation. An integrated knowledge graph semantic web service (KGSWS) repository was constructed from 48 OWLS-TC v4 ontologies containing 1083 semantic web services. In Phase 1, TransE, ComplEx, and DistMult were optimized over KGSWS to learn semantic representations through link prediction evaluation. Among the evaluated models, TransE achieved the best embedding quality with MRR of 0.5792 and Hits@10 value of 0.6716. In Phase 2, the learned representations were evaluated using different clustering techniques to support candidate search-space reduction prior to service ranking. In Phase 3, recommendation performance was evaluated using 38 benchmark queries in terms of Precision@10, Recall@10, NDCG@10, and MAP@10. The TransE + K-Means configuration obtained average values of 0.9579, 0.7207, 0.9667, and 0.9873, respectively. Differences among the evaluated configurations were further examined using the Friedman test followed by Dunn–Bonferroni post hoc analysis. For the evaluated repository settings, the scalability analysis obtained a search-space reduction of 82.73
