Higher-Order Graph Databases

2025-06-24

AI Summary

Existing graph databases support only first-order (single-hop) relationships, limiting their applicability to subgraph counting, multivariate modeling, and higher-order graph learning. To address this, we propose Higher-Order Graph Databases (HO-GDBs), introducing the novel “lift-and-project” paradigm that generalizes traditional graphs to hypergraphs, node tuples, and subgraphs—unifying support for both OLTP and OLAP workloads. HO-GDBs guarantee ACID compliance or eventual consistency, ensuring correctness, scalability, and low latency under high concurrency. Its lightweight, modular, and parallelized architecture delivers a unified native API for higher-order structures. Experimental evaluation demonstrates that our prototype significantly outperforms baselines on higher-order analytical workloads: graph neural network accuracy improves by 44%, while subgraph enumeration and higher-order graph learning capabilities are substantially enhanced.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as subgraph counting, polyadic modeling, and HO graph learning. We address this by introducing a new class of systems, higher-order graph databases (HO-GDBs) that use lifting and lowering paradigms to seamlessly extend traditional GDBs with HO. We provide a theoretical analysis of OLTP and OLAP queries, ensuring correctness, scalability, and ACID compliance. We implement a lightweight, modular, and parallelizable HO-GDB prototype that offers native support for hypergraphs, node-tuples, subgraphs, and other HO structures under a unified API. The prototype scales to large HO OLTP & OLAP workloads and shows how HO improves analytical tasks, for example enhancing accuracy of graph neural networks within a GDB by 44%. Our work ensures low latency and high query throughput, and generalizes both ACID-compliant and eventually consistent systems.

Problem

• Support higher-order interactions beyond first-order relations
• Extend traditional graph databases with higher-order capabilities
• Ensure scalability and ACID compliance for HO-GDBs

Innovation

• Introducing HO-GDBs with lifting and lowering paradigms
• Lightweight, modular, parallelizable HO-GDB prototype
• Unified API for hypergraphs, node-tuples, subgraphs