A Unified Hypergraph- and SuperHyperGraph-Based Framework for Food Web Extension: From Classical Food Webs to SuperHyperWebs in Agricultural and Ecological Systems - Fujita, Takaaki (Management Analytics and Social Insights, 2025)
Research on the applications of graph theory has also been conducted in areas such as Agriculturaland Ecological Systems. Hypergraphs generalize graphs by allowing hyperedges to join any numberof vertices, while superhypergraphs further extend this idea by layering iterated powersets to capturehierarchical, self-referential connections. A food web models an ecosystem as a directed graph whosenodes are species and whose edges represent predator–prey interactions. In this paper, we introduce twonovel extensions of classical food webs: the Food HyperWeb, which encodes each predator’s entire prey setas a hyperedge, and the Food n-SuperHyperWeb, which embeds multilevel trophic relationships within ann-fold superhypergraph structure. We provide formal definitions, establish their foundational properties,and present illustrative examples demonstrating their effectiveness for agricultural and ecological networkanalysis.