Representing Higher-Order Networks: A Survey of Graph-Based Frameworks

• URL: http://arxiv.org/abs/2605.12509v2
• Date: Fri, 15 May 2026 13:29:23 GMT
• Title: Representing Higher-Order Networks: A Survey of Graph-Based Frameworks
• Abstract summary: This book presents a comprehensive overview of mathematical notions that can be used to model higher-order networks.<n>It surveys foundational concepts, extensional frameworks, and newly introduced formalisms.<n>The aim is to help readers compare diverse higher-order network models and identify appropriate tools for theoretical study and practical applications.
• Score: 2.2667044928324747
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order graph formalisms extend this framework by incorporating multiway, hierarchical, temporal, multilayer, recursive, and tensor-based interactions, thereby providing more expressive representations of complex systems. This book presents a comprehensive overview of mathematical notions that can be used to model higher-order networks. It surveys foundational concepts, extensional frameworks, and newly introduced formalisms, with an emphasis on their structural principles, relationships, and modeling roles. The aim is to provide a unified perspective that helps readers compare diverse higher-order network models and identify appropriate tools for theoretical study and practical applications. This book is Edition 2.0. It mainly includes the addition of several concepts, as well as corrections and improvements of typographical errors and explanations.

Related papers

• Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence [51.30336200738606]
  There is strong agreement that Graph Foundation Models (GFMs) are essential for advancing graph learning.<n> considerable disagreement persists on how to build a powerful, general-purpose GFM analogous to Large Language Models (LLMs)
  arXiv  Detail & Related papers  (2026-03-23T05:49:19Z)
• UniG2U-Bench: Do Unified Models Advance Multimodal Understanding? [50.92401586025528]
  Unified multimodal models have recently demonstrated strong generative capabilities, yet whether and when generation improves understanding remains unclear.<n>We introduce UniG2U-Bench, a comprehensive benchmark categorizing generation-to-understanding (G2U) evaluation into 7 regimes and 30 subtasks.
  arXiv  Detail & Related papers  (2026-03-03T18:36:16Z)
• Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods [0.12289361708127876]
  This survey provides a comprehensive review of methods handling n-ary relational data, covering both knowledge hypergraphs and hyper-relational knowledge graphs literatures.<n>We propose a two-dimensional taxonomy: the first dimension categorises models based on their methodology, i.e., translation-based models, deep neural network-based models, logic rules-based models, and hyperedge expansion-based models.<n>The second dimension classifies models according to their awareness of entity roles and positions in n-ary relations, dividing them into aware-less, position-aware, and role-aware approaches.
  arXiv  Detail & Related papers  (2025-06-05T22:59:39Z)
• In-situ graph reasoning and knowledge expansion using Graph-PReFLexOR [0.0]
  We present Graph-PReFLexOR, a framework that combines graph reasoning with symbolic abstraction to dynamically expand domain knowledge.<n>Inspired by reinforcement learning, it defines reasoning as a structured mapping, where tasks yield knowledge graphs, abstract patterns, and ultimately, final answers.<n>Results show superior reasoning depth and adaptability, underscoring the potential for transparent, multidisciplinary AI-driven discovery.
  arXiv  Detail & Related papers  (2025-01-14T13:52:41Z)
• Towards Graph Foundation Models: Training on Knowledge Graphs Enables Transferability to General Graphs [26.477872205199667]
  We introduce SCR, a unified graph reasoning framework designed to train on knowledge graphs.<n>We propose semantic-conditioned message passing, a novel mechanism addressing the inherent semantic isolation in traditional KG reasoning.<n>Our results show substantial performance gains over existing foundation models.
  arXiv  Detail & Related papers  (2024-10-16T14:26:08Z)
• Foundations and Frontiers of Graph Learning Theory [81.39078977407719]
  Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. This article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models.
  arXiv  Detail & Related papers  (2024-07-03T14:07:41Z)
• Graph Foundation Models: Concepts, Opportunities and Challenges [66.37994863159861]
  Foundation models have emerged as critical components in a variety of artificial intelligence applications.<n>The capabilities of foundation models in generalization and adaptation motivate graph machine learning researchers to discuss the potential of developing a new graph learning paradigm.<n>This article introduces the concept of Graph Foundation Models (GFMs), and offers an exhaustive explanation of their key characteristics and underlying technologies.
  arXiv  Detail & Related papers  (2023-10-18T09:31:21Z)
• Weisfeiler and Leman Go Relational [4.29881872550313]
  We investigate the limitations in the expressive power of the well-known GCN and Composition GCN architectures. We introduce the $k$-RN architecture that provably overcomes the limitations of the above two architectures.
  arXiv  Detail & Related papers  (2022-11-30T15:56:46Z)
• Hyperbolic Graph Neural Networks: A Review of Methods and Applications [61.49208407567829]
  This survey paper provides a comprehensive review of the rapidly evolving field of Hyperbolic Graph Learning (HGL)<n>We systematically categorize and analyze existing methods dividing them into (1) hyperbolic graph embedding-based techniques, (2) graph neural network-based hyperbolic models, and (3) emerging paradigms.<n>We extensively discuss diverse applications of HGL across multiple domains, including recommender systems, knowledge graphs, bioinformatics, and other relevant scenarios.
  arXiv  Detail & Related papers  (2022-02-28T15:08:48Z)
• Tensor Graph Convolutional Networks for Multi-relational and Robust Learning [74.05478502080658]
  This paper introduces a tensor-graph convolutional network (TGCN) for scalable semi-supervised learning (SSL) from data associated with a collection of graphs, that are represented by a tensor. The proposed architecture achieves markedly improved performance relative to standard GCNs, copes with state-of-the-art adversarial attacks, and leads to remarkable SSL performance over protein-to-protein interaction networks.
  arXiv  Detail & Related papers  (2020-03-15T02:33:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.