Signaling SuperHypergraph

Abstract

Graph theory studies mathematical structures of vertices and edges to model relationships and connectivity [1, 2]. Hypergraphs extend traditional graphs by allowing hyperedges that connect any number of vertices simultaneously [3,4]. Superhypergraphs further generalize this idea through iterated powerset layers, enabling hierarchical and self-referential connections among hyperedges [5–7]. Graph theory is also extensively used in biology, biochemistry, and related fields (cf. [8,9]). A Signaling Graph is a directed graph in which vertices represent entities and edges denote activation or inhibition of targets. A Signaling Hypergraph generalizes signaling graphs by using hyperedges that link sets of regulators to sets of targets in reactions [10–13]. In this paper, we define the Signaling ?-SuperHypergraph, which extends these concepts using superhypergraphs, and we briefly examine its properties. Although this work is purely theoretical, we hope that future research will further advance hierarchical modeling in complex systems.