The current of development in 20th century logic bypassed Peirce’s existential graphs, but recently much good work has been done by formal logicians excavating the graphs from Peirce’s manuscripts, regularizing them and demonstrating the soundness and completeness of the alpha and beta systems (e.g. Roberts 1973, Hammer 1998, Shin 2002). However, given that Peirce himself considered the graphs to be his ‘chef d’oeuvre’ in logic, and explored the distinction between icons, indices and symbols in detail within the context of a much larger theory of signs, much about the graphs arguably remains to be thought through from the perspective of philosophical logic. For instance, are the graphs always merely of heuristic value or can they convey an ‘essential icon’ (analogous to the now standardly accepted ‘essential indexical’)? This paper claims they can and do, and suggests important consequences follow from this for the epistemology of modality. It is boldly suggested that structural articulation, which is characteristic of icons alone, is the source of all necessity. In other words, recognizing a statement as necessarily true consists only in an unavoidable recognition that a structure has the particular structure that it in fact has. (What else could it consist in?)