In graph theory, a **bound graph** expresses which pairs of elements of some partially ordered set have an upper bound. Rigorously, any graph *G* is a bound graph if there exists a partial order ≤ on the vertices of *G* with the property that for any vertices *u* and *v* of *G*, *uv* is an edge of *G* if and only if *u* ≠ *v* and there is a vertex *w* such that *u* ≤ *w* and *v* ≤ *w*.

Bound graphs are sometimes referred to as *upper bound graphs*, but the analogously defined **lower bound graphs** comprise exactly the same class—any lower bound for ≤ is easily seen to be an upper bound for the dual partial order ≥.