Graph of Desire

A four-stage diagram building from the simplest possible model of Signification to a fully articulated map of how Desire, Demand, the Other, and Jouissance interlock. Lacan presents it across Seminars V–VI and freezes its final form in the Écrits essay "Subversion of the Subject" (1960).

The graph is built up, not given all at once. Each version adds a layer. Reading the final form without working through the earlier versions is futile — the layers are not independently legible.

Stage 1 — the elementary cell

                   S(O) ←─── O
                    │
                    │  (signifying chain
                    │   crosses the bar)
                    ↓
                    s(O) ←─── intention

The simplest model: a Signifier (S) crosses an intention arc and ends up producing a signified (s). The intention is the speaker's pre-symbolic motive; the signifier is the chain it must pass through; the signified is the retroactive meaning produced. This is the Point de capiton in microcosm.

Two crossings: where the intention meets the chain (entering symbolic order), and where it returns (the meaning effect).

Stage 2 — the Other enters

                   S(O) ←─── O                ← upper line: enunciation
                    │
                    ↓
                    s(O)        ← signified, now the "message"
                    ↑
                   ∆ ─── Other(o)             ← lower line: enounced

      (vector ∆ → signifier(O) crosses lower bar = code;
       crossing upper bar produces s(O) = message)

The intention is now ∆ ("Need"). The Other appears at o on the lower line: the locus of the Signifier. The crossing produces both a code (the lower-line crossing — the symbolic resources available) and a message (the upper-line crossing — the produced meaning).

The Subject in formation passes through the Other twice — once to enter language at all, once to return as the meaning of what's been said.

Stage 3 — adding desire

The graph develops a second floor. Above the message line a new line is added, where desire and the Other meet at higher levels of articulation:

       Upper:   $ ◇ a ─── d (Desire) ─── S(Ⱥ) ←── (Other lacks)
                  │                        │
                  │                        │
                  ↓                        ↓
       Lower:   s(O) ─── O ─── i(o) ─── m (ego)

                ($ ◇ a is the formula of fantasy;
                 d is desire as such, distinguished from
                 demand; S(Ⱥ) is the signifier of the
                 Other's lack)

The upper level is not separate from the lower — it's the same circuit, taken at the level of what the Other lacks. Demand goes around the lower circuit ("give me what you have"); desire arises in the gap between demand and what the Other actually has — and points at what the Other lacks.

Stage 4 — the complete graph

The final form (in "Subversion of the Subject") adds Jouissance and Castration:

                    Jouissance        Castration
                         │                │
                         ↓                ↓
                    S(Ⱥ) ──────── ($ ◇ D)               ← upper level
                         │                │
                         ↓                ↓
       d ─── ($ ◇ a)                                    ← desire / fantasy
                         │
       ────────────────────────────                     ← message / signified
                         │                │
                  s(O) ───── O ───── i(o) ─── m         ← lower / ego level
                                              │
                                              ↓
                                          ∆ (Need)

This is the diagram you'll see most often cited. Reading it requires keeping track of:

∆ at the bottom right: the pre-symbolic Need.
m (ego) just above: where need first gets caught in imaginary capture.
i(o): the imaginary other, the Mirror Stage image.
s(O) and O on the lower line: the symbolic register where Demand articulates.
d: Desire as the gap between demand and what the Other can give.
$ ◇ a: the Fantasy formula — the Subject in relation to Objet petit a.
S(Ⱥ) at upper left: the signifier of the lack in the Other.
$ ◇ D: the subject's relation to the signifying chain of demand, taken as a whole.
Jouissance and Castration at the top: the upper limit, the level where the symbolic exceeds itself.

What it claims

The subject is constituted in stages. From need through demand through desire — each level retroactively reorganizes the levels below.
Meaning is retroactive. A sentence's meaning is fixed only when it's complete; the Point de capiton traverses the bar from chain to message backward in time.
Desire is not demand. Demand asks for an object; desire is what's left over when the object is given. Desire's true target is the Other's lack, not any particular object.
Fantasy organizes the subject's relation to lack. The formula $ ◇ a is the structural support of the subject — what holds the subject in relation to its lost object.
The Other lacks too. The upper-level S(Ⱥ) is what this graph teaches even more clearly than the L Schema does: there is no Other of the Other. The symbolic is not guaranteed by anything outside it.

Where Lacan introduces / develops it

Seminar V: Formations of the Unconscious (1957–58) (Seminar V · Formations of the UnconsciousJacques Lacan · 1957) — early stages
Seminar VI: Desire and Its Interpretation (1958–59) (Seminar VI · Desire and Its InterpretationJacques Lacan · 1958) — substantial development
Écrits: "The Subversion of the Subject and the Dialectic of Desire in the Freudian Unconscious" (1960) — final form
Seminar VII: The Ethics of Psychoanalysis (Seminar VII · The Ethics of PsychoanalysisJacques Lacan · 1959) — the graph is referenced, not redrawn

Concepts deployed

Subject · Desire · Demand · Need · The big Other · Signifier · Signification · Fantasy · Objet petit a · Jouissance · Castration · Splitting of the Subject · Point de capiton · Mirror Stage · Ego

Interpretive traps

Trying to read the final graph cold. It can't be done. Read the four stages in order, with Bruce Fink's commentary in The Lacanian Subject alongside.
Treating the upper and lower levels as separate circuits. They are the same circuit at different levels of articulation. Lacan is explicit: desire and demand traverse the same path, only the level of what's at stake changes.
Reading the graph as developmental. It is structural, not chronological. The newborn does not literally pass through stage 1, then stage 2, etc. The stages are layers always already operating in the speaking subject.
Forgetting it's eclipsed by the Borromean Knot in late Lacan. The Graph of Desire is mid-period (~1960). By Encore (1972), Lacan no longer foregrounds it. It remains a reference for the middle-period theory of desire.