Representing Higher-Order Networks: A Survey of Graph-Based Frameworks
For researchers and practitioners in network science, this survey offers a unified perspective to compare and select higher-order network models, but it is an incremental update (Edition 2.0) with minor additions and corrections.
This survey provides a comprehensive overview of mathematical frameworks for modeling higher-order networks, including multiway, hierarchical, temporal, and tensor-based interactions, aiming to unify diverse models for theoretical and practical use.
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.