community detection

This study addresses the limitation of traditional network analysis—which operates primarily at the node level and fails to capture coexisting community-level structural patterns—by proposing the first community-level core-periphery detection framework tailored to collaborative networks. Methodologically, it jointly optimizes community partitioning and role assignment through an objective function that models both inter-community connection density and strength, enabling attribute-driven interpretation (e.g., disciplinary or geographical) of collective roles. Empirical evaluation on an Italian co-authorship network demonstrates that the framework effectively uncovers hierarchical core-periphery structures tightly linked to institutional status, regional development, and research themes, while quantifying structural inequality in scientific collaboration. By transcending the node-centrality paradigm, this work provides a novel, structurally grounded perspective for analyzing organizational mechanisms underlying knowledge diffusion and innovation emergence.

In practical applications, community detection methods lack standardized evaluation protocols, and their impact on downstream graph mining tasks is often overlooked. This paper systematically investigates how diverse community detection algorithms affect the performance of link prediction and node classification. We propose a unified, extensible evaluation framework that integrates structured community feature extraction, statistical analysis, and machine learning modeling to enable cross-algorithm performance comparison. Experimental results across multiple benchmark datasets demonstrate that algorithm selection significantly influences downstream task accuracy, with distinct methods exhibiting pronounced strengths and weaknesses depending on the specific task. Our framework provides reproducible, empirically grounded guidance for selecting appropriate community detection methods tailored to concrete application scenarios, thereby bridging the gap between community detection research and real-world graph analytics. (149 words)

Existing hypergraph clustering coefficients treat hyperedges as atomic units, ignoring pairwise interactions among their constituent nodes—leading to spurious zero values for nodes embedded in nontrivial clustering structures. Method: We propose a novel hypergraph clustering coefficient that explicitly models intra-hyperedge pairwise relational strength via a mapping from hypergraphs to weighted graphs. Contribution/Results: The proposed coefficient rigorously satisfies three theoretical desiderata: (i) boundedness in [0,1], (ii) consistency with the classical graph clustering coefficient upon graph degeneration, and (iii) faithful characterization of higher-order local structure. Validated through higher-order motif analysis and real-world social and collaboration datasets, it significantly corrects the zero-value bias of conventional methods on 3-node motifs (III, IV-a, IV-b) and provides finer-grained, more accurate quantification of local density—especially for large hyperedges.

To address the challenge of jointly detecting communities in multilayer networks (e.g., temporal, multi-view, or independently sampled networks), where heterogeneous connection patterns coexist with shared community structures, this paper proposes the Multilayer Degree-Corrected Stochastic Block Model (ML-DCSBM). We establish its identifiability theory for the first time and prove that the misclustering rate of joint spectral clustering decays exponentially with the number of layers. Methodologically, we achieve efficient joint spectral clustering via eigenvector concatenation and normalization, simultaneously accommodating degree heterogeneity and inter-layer variation in block connectivity matrices. Theoretically, we derive tight error bounds and demonstrate enhanced robustness to layer-specific noise and sparsity. Empirically, our method significantly outperforms state-of-the-art approaches on synthetic benchmarks and successfully uncovers dynamic community evolution and node centrality shifts in the U.S. airport network from 2016–2021, revealing structural resilience and adaptation under pandemic-induced disruptions.

This work addresses the challenge of simultaneously performing network-level clustering and node-level community detection in multi-network analysis. We propose the first Bayesian nonparametric model based on the nested Dirichlet process (NDP), enabling joint inference of both the number of network types and the number of communities within each network. The model accommodates unlabeled, structurally heterogeneous networks with unequal node sets—overcoming key limitations in modeling anonymized nodes and scale-heterogeneous networks. We develop three Gibbs samplers—standard, collapsed, and blocked—to ensure efficient posterior inference. Extensive experiments demonstrate that the method accurately recovers hierarchical clustering structures on synthetic data and achieves superior performance on two real-world social network datasets. To our knowledge, this is the first unified, adaptive, and scalable framework for multi-network co-analysis, offering principled uncertainty quantification and automatic complexity control without requiring prespecified numbers of clusters or communities.

To address the inherent trade-off between high precision and high recall in community detection, this paper proposes a novel ensemble framework. First, it introduces DSC-Flow-Iter—a local clustering algorithm that iteratively extracts dense subgraphs and refines results via flow-based optimization—achieving high precision but low recall. Second, it integrates this with a modularity-optimization method known for high recall but lower precision, forming a complementary ensemble strategy. The framework unifies heterogeneous clustering outputs through a weighted consensus mechanism and structural correction. Extensive evaluation on synthetic benchmarks demonstrates that the proposed approach significantly outperforms individual algorithms and state-of-the-art baselines in both F1-score and normalized mutual information (NMI), with average improvements of 12.6%. It exhibits superior accuracy and robustness, offering a scalable, multi-objective-balanced paradigm for community discovery.

Spectral clustering suffers significant performance degradation on core-periphery structured networks—particularly under sparsity—due to inadequate modeling of sparse inter-layer connections by existing adjacency spectral embedding (ASE) methods. To address this, we propose Double Adjacency Spectral Embedding (DASE), the first method to construct the embedding space using the square of the adjacency matrix, thereby enhancing representation fidelity for sparse cross-core-periphery links. We establish theoretical consistency of DASE under the degree-corrected stochastic block model (DCSBM) with varying sparsity levels. Empirical evaluation on synthetic benchmarks and real-world employment and transportation networks demonstrates that DASE consistently outperforms both ASE and Laplacian spectral clustering: it achieves average accuracy improvements of 12–28% on core-periphery structures, while exhibiting superior robustness to sparsity and strong generalization across diverse network domains.

Spectral clustering lacks rigorous theoretical analysis for graphs with hierarchical or directed structures. Method: We propose a general performance criterion based on spectral gaps: accurate recovery of multiscale and directionally coherent clusters is guaranteed when the smallest eigenvalues of a Hermitian matrix representation form well-separated groups from the rest of the spectrum. Our approach transcends traditional Laplacian-based frameworks by extending spectral clustering theory to arbitrary Hermitian matrix representations—including Hermitianized formulations for directed graphs—and integrates symmetric graph representations with spectral graph theory via eigenvalue decomposition and spectral gap analysis. Contribution/Results: The resulting theory yields verifiable, interpretable guarantees. Experiments demonstrate that it accurately predicts clustering performance on synthetic benchmarks and real-world ecological networks (e.g., trophic level inference), significantly enhancing the interpretability and applicability of spectral clustering on complex-structured graphs.

This study addresses the challenge of applying conventional statistical methods to collections of heterogeneous networks that vary in size and type and lack node correspondence. To overcome this, the authors propose a functional Topological Data Analysis (funTDA) framework that uniquely integrates functional data analysis with persistent homology to extract topological features from networks. This approach enables standard statistical operations—including mean and variance estimation, principal component analysis, and hypothesis testing—despite the non-Euclidean nature of network structures, thereby establishing a unified inferential framework. Empirical evaluations demonstrate that funTDA effectively discriminates networks with distinct connectivity patterns and successfully uncovers significant topological differences in real-world applications, such as literary co-occurrence networks and influenza gene regulatory networks.

Existing geometric approaches (e.g., spectral embedding) for community detection in complex networks neglect topological structure, while topological methods (e.g., ToMATo) rely heavily on initial projections, limiting robustness and adaptability. Method: This paper proposes the first geometric–topological dual-paradigm framework: it constructs a density landscape in the spectral embedding space and jointly leverages persistent homology and density basin detection to adaptively select optimal community partitions. Contribution/Results: (i) It is the first work to integrate topological data analysis (TDA) into the geometric embedding pipeline, enabling joint modeling of topological features and intrinsic geometric structure; (ii) it introduces a modularity-guided persistent community extraction mechanism, mitigating structural blind spots inherent to single-paradigm methods. On synthetic benchmarks, the framework achieves modularity comparable to Louvain, while significantly improving accuracy and robustness in detecting geometry-sensitive communities.