A graph can specify the skeletal structure of an idea, onto which meaning can be added by interpreting the structure. This paper considers several directed and undirected graphs consisting of four nodes, and suggests different meanings that can be associated with these different structures. Drawing on John G. Bennett’s “systematics,” specifically on the Tetrad that systematics offers as a model of “activity,” the analysis formalizes and augments the systematics account and shows that the Tetrad is a versatile model of problem-solving, regulation and control, and other processes. Discussion is extended to include hypergraphs, in which links can relate more than two nodes, and the possibility of a “reconstructability analysis of ideas” is suggested.