Research Article

River Network HyperGraphs and Transportation Network HyperGraphs: A Graph-Theoretic Approach for Geoscientific and Civil Applications

Abstract

River Network Graphs and Transportation Network Graphs are classical models that represent river systems and transportation infrastructures as vertices and edges, respectively, and underpin applications in hydrological simulation, watershed management, shortest-path computation, and urban traffic analysis. In this paper, we extend these graph-based models into the hypergraph and superhypergraph domains by introducing two new structures—River Network HyperGraph and Transportation Network HyperGraph—and their hierarchical generalizations, River Network SuperHyperGraph and Transportation Network SuperHyperGraph. These enhanced representations enable multi-scale, hierarchical modeling of waterway and transportation networks, offering a unified framework for advanced analysis and management of complex infrastructure systems.