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

Takaaki Fujita 

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.