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A syntactic dependency is a typed relation between an expression and its syntactic head under an explicit grammatical representation. In basic Universal Dependencies, the words form a rooted tree: one word attaches to a notional ROOT, and each other word has one basic head. An enhanced representation can instead form a more general graph.^[ref]

For the original example The small birds fly, number the words one through four. In head-to-dependent notation, the links are 4→3 for the subject, 3→1 for the determiner, and 3→2 for the adjective; 0→4 identifies the sentence head. The determiner link spans a nonadjacent word, showing why dependency is not merely adjacency.

The direction of an arrow and the meaning of each relation must be stated. The project also notes that some dependency labels encode relationships without asserting a simple head-subordinate linguistic analysis. A mechanically valid tree therefore remains a representation to justify, rather than a proof of its own grammatical interpretation.

A syntactic head is the element treated as central to a construction under a specified structural analysis. It can determine grammatical properties or which other elements may occur. Headedness therefore concerns relationships within a construction, beyond which word seems most informative in the conversation.^[ref]

In a conventional noun-headed analysis of the small boxes, boxes heads the noun phrase. The head's plural grammatical number helps explain the grammatical agreement in The small boxes are ready. Changing small to heavy changes the description without changing that number requirement.

In a dependency representation, a head also provides the attachment point for syntactic dependencies. A reproducible analysis states its conventions: different grammatical frameworks can choose different heads for some constructions. The success of a representation depends on the patterns it explains and predicts, not solely on whether its links form a mechanically valid rooted tree.