Graphs are basically diagrams, but importantly so are algebraic expressions, and this points to an operational conception of diagrammatic signs beyond their descriptive foundation in similarity relations. The graph-image is exposed to cognitive operations valid for images such as mental rotation and mirror image formation. For Charles Sanders Peirce, diagrammatic reasoning is inherently mathematical in this sense of necessary reasoning. Peirce struggled all his life with this tension between semiotics as a logic of reasoning and semiotics as a construction of meaning within different genres and domains of discourse. The ambiguity that arises for the Existential Graphs between an operational iconic logic versus a diagrammatic reasoning with ontological implications can be seen as an instance of this general tension. Graphs and algebra are iconic forms associated with “necessary reasoning”. A strange phenomenon has been observed in science learning: Students who adopt a “surface approach” to learning attempt to remember graphs independent of the models they represent.