Multi-SuperHyperGraph Neural Networks: A Generalization ofMulti-HyperGraph Neural Networks

Abstract

Graph theory provides a mathematical framework for modeling relationships among entities via
vertices (nodes) and edges [1, 2]. A hypergraph extends this framework by allowing hyperedges to connect
any number of vertices, thereby capturing complex multi-way interactions [3]. The SuperHyperGraph concept
generalizes hypergraphs further through iterated power-set constructions and has recently drawn significant
research interest [4, 5].
Graph Neural Networks (GNNs) propagate and aggregate node features across graph topologies via learn-
able message-passing to capture structural context [6–8]. Extensions such as Hypergraph Neural Networks,
SuperHyperGraph Neural Networks, Multigraph Neural Networks, and MultiHyperGraph Neural Networks
have likewise been explored [9, 10].
In this paper, we introduce and analyze the Multi n-SuperHyperGraph Neural Network, a theoretical extension
of SuperHyperGraph Neural Networks built upon Multi-SuperHyperGraph structures. We expect that this
framework will stimulate further advances in the study and application of GNNs