Graph theory studies the mathematical structures of vertices and edges to model relationships and connectivity 1, 2. Hypergraphs extend this framework by allowing hyperedges to connect arbitrarily many vertices at once 3, and superhypergraphs further generalize hypergraphs via iterated powerset constructions to capture hierarchical linkages among edges 4,5. Weighted multidimensional networks model nodes connected by edges in multiple layers, assigning each edge a weight to quantify relationship strength in its specific dimension(cf. 6,7). In this paper, we extend these ideas using hypergraphs and superhypergraphs to introduce and formalize multidimensional hypernetworks and multidimensional superhypernetworks.
Takaaki Fujita (Sat,) studied this question.