Extending Factor, Signal Flow, Control Flow, Dataflow, and PERT/CPM Graphs to Hypergraphs and Superhypergraphs

Abstract

Graph theory investigates how vertices and edges model relationships and connectivity [1, 2]. Hypergraphs extend this paradigm by permitting hyperedges that join any number of vertices [3], and superhypergraphs further generalize via iterated powerset constructions to capture nested, hierarchical linkages among edges [4,5]. Graphs are ubiquitous across many disciplines. In this paper, we show how five classical graph models—factor graphs, signal flow graphs, control flow graphs, dataflow graphs, and PERT/CPM graphs—can be lifted into the HyperGraph and SuperHyperGraph frameworks, and we present illustrative examples for each. These extensions open the door to systematic, multi-level modeling of complex applications.