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

2025-07-11

AI Summary

Efficient online discovery of (k,g)-cores—higher-order cohesive substructures—in large-scale hypergraphs suffers from high computational cost and sensitivity to the higher-order connectivity parameter g. Method: We propose the first lightweight incremental indexing framework supporting tunable g, avoiding global traversal. Leveraging the formal definition of (k,g)-cores, we design a compact index structure that integrates local expansion and pruning, enabling online decomposition and querying by accessing only relevant hyperedges. Contribution/Results: Our approach is the first to embed g as a controllable parameter within the indexing mechanism, balancing flexibility and efficiency. Both index construction and query processing achieve sublinear time complexity. Extensive experiments on multiple real-world hypergraphs demonstrate that our method reduces query latency by 1–2 orders of magnitude and decreases index space overhead by 40%–65% over state-of-the-art baselines, significantly enabling real-time higher-order relational analysis on large-scale hypergraphs.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Distributed Search
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Web Mining and Content Analysis: Topic discovery and tracking
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

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.

Problem

• Efficient computation of cohesive subgraphs in large hypergraphs
• Online retrieval of high-order cohesive structures without exhaustive traversal
• Parameter selection for cohesive subgraph discovery in complex networks

Innovation

• Efficient indexing structure for hypergraphs
• Online cohesive subgraph retrieval method
• Avoids exhaustive graph traversal for speed