Autosegmental phonology represents words with graph structures. This paper introduces a way of reasoning about autosegmental graphs as strings of concatenated graph primitives. The main result shows that the sets of autosegmental graphs so generated obey two important, putatively universal, constraints in phonological theory provided that the graph primitives also obey these constraints. These constraints are the Obligatory Contour Principle and the No Crossing Constraint. Thus, these constraints can be understood as being derived from a finite basis under concatenation. This contrasts with (and complements) earlier analyses of autosegmental representations, where these constraints were presented as axioms of the grammatical system. Empirically motivated examples are provided.