arXiv subjects

Song Kim

Publications and source records attributed to Song Kim.

5 recordsLinked to original sources

arXiv2026

Efficient Computation of Maximum Flexi-Clique in Networks

Discovering large cohesive subgraphs is a key task for graph mining. Existing models, such as clique, k-plex, and {\gamma}-quasi-clique, use fixed density thresholds that overlook the natural decay of connectivity as the subgraph size increases. The Flexi-clique model overcomes this limitation by imposing a degree constraint that grows sub-linearly with subgraph size. We provide the algorithmic study of Flexi-clique, proving its NP-hardness and analysing its non-hereditary properties. To address its computational challenge, we propose the Flexi-Prune Algorithm FPA, a fast heuristic using core-based seeding and connectivity-aware pruning, and the Efficient Branch-and-Bound Algorithm EBA, an exact framework enhanced with multiple pruning rules. Experiments on large real-world and synthetic networks demonstrate that FPA achieves near-optimal quality at much lower cost, while EBA efficiently computes exact solutions. Flexi-clique thus provides a practical and scalable model for discovering large, meaningful subgraphs in complex networks.

cs.SI↗

arXiv2025

Experimental Analysis and Evaluation of Cohesive Subgraph Discovery

Retrieving cohesive subgraphs in networks is a fundamental problem in social network analysis and graph data management. These subgraphs can be used for marketing strategies or recommendation systems. Despite the introduction of numerous models over the years, a systematic comparison of their performance, especially across varied network configurations, remains unexplored. In this study, we evaluated various cohesive subgraph models using task-based evaluations and conducted extensive experimental studies on both synthetic and real-world networks. Thus, we unveil the characteristics of cohesive subgraph models, highlighting their efficiency and applicability. Our findings not only provide a detailed evaluation of current models but also lay the groundwork for future research by shedding light on the balance between the interpretability and cohesion of the subgraphs. This research guides the selection of suitable models for specific analytical needs and applications, providing valuable insights.

cs.SI↗

arXiv2025

Uncovering High-Order Cohesive Structures: Efficient (k,g)-Core Computation and Decomposition for Large Hypergraphs

Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the fundamental problems and offers deep insights into these structures, yet the task of selecting appropriate parameters is an open question. To address this question, we aim to design an efficient indexing structure to retrieve cohesive subgraphs in an online manner. The main idea is to enable the discovery of corresponding structures within a reasonable time without the need for exhaustive graph traversals. Our method enables faster and more effective retrieval of cohesive structures, which supports decision-making in applications that require online analysis of large-scale hypergraphs. Through extensive experiments on real-world networks, we demonstrate the superiority of our proposed indexing technique.

cs.SI↗

arXiv2025

Cohesive Subgraph Discovery in Hypergraphs: A Locality-Driven Indexing Framework

Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the fundamental problems and offers deep insights into these structures, yet the task of selecting appropriate parameters is an open question. To handle that question, we aim to design an efficient indexing structure to retrieve cohesive subgraphs in an online manner. The main idea is to enable the discovery of corresponding structures within a reasonable time without the need for exhaustive graph traversals. This work can facilitate efficient and informed decision-making in diverse applications based on a comprehensive understanding of the entire network landscape. Through extensive experiments on real-world networks, we demonstrate the superiority of our proposed indexing technique.

cs.SI↗

arXiv2023

Symphony: Symmetry-Equivariant Point-Centered Spherical Harmonics for 3D Molecule Generation

We present Symphony, an $E(3)$-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for molecules utilize rotationally invariant features to respect the 3D symmetries of molecules. In contrast, Symphony uses message-passing with higher-degree $E(3)$-equivariant features. This allows a novel representation of probability distributions via spherical harmonic signals to efficiently model the 3D geometry of molecules. We show that Symphony is able to accurately generate small molecules from the QM9 dataset, outperforming existing autoregressive models and approaching the performance of diffusion models.

cs.LG↗