The graph of desire is a topological model of the structure of desire.
Jacques Lacan began to develop the graph of desire in his 1957-58 seminar, Les formations de l'inconscient. The graph of desire reappears in some of the following seminars in various forms, although the most well known form of it appears in "The Subversion of the Subject and the Dialectic of Desire in the Freudian Unconscious."
In this paper, Lacan builds up the graph of desire in four stages.
The first of these stages in the "elementary cell" of the graph.
The horizontal line represents the diachronic signifying chain; the horseshoe-shaped line represents the vector of the subject's intentionality.
The double intersection of these two lines illustrates the nature of retroaction: the message, at the point marked s(A) in the elementary cell, is the point de capiton determined retroactively by the particular punctuation given to it by the Other, A.
The prelinguistic mythical subject of pure need, indicated by the triangle, must pass through the defiles of the signifier which produces the divided subject, $.
The intermediate stages of the graph of desire are not meant to show any evolution or temporal development, since the graph always exists as a whole; they are simply pedagogical devices used by Lacan in order to illustrate the structure of the complete graph.
Nevertheless, Lacan never intended to describe the genetic stages of a biological development.
Rather, it represents the "logical moments" of the birth of a speaking subject.
In the completed graph there are not one but two signifying chains.
The lower chain (from the signifier to the voice) is the conscious signifying chain, the level of the statement.
The upper chain (from jouissance to castration) is the signifying chain in the unconscious, the level of the enunciation.
The structure is thus duplicated: the upper part of the graph is structured exactly like the lower part.