An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's Collected Papers.
The syntax is:
The semantics are:
A "proof" manipulates a graph, using a short list of rules, until the graph is reduced to an empty cut or the blank page. A graph that can be so reduced is what is now called a tautology (or the complement thereof). Graphs that cannot be simplified beyond a certain point are analogues of the satisfiable formulas of first-order logic.
Peirce soon abandoned the entitative graphs for the existential graphs, whose sentential (alpha) part is dual to the entitative graphs. He developed the existential graphs until they became another formalism for what are now termed first-order logic and normal modal logic.
The primary algebra of G. Spencer-Brown is isomorphic to the entitative graphs.