AbstractA function diagram (f-diagram) D consists of the family of curves {1̵ñ} obtained from n continuous functions fi:[0,1]→R(1⩽i⩽n). We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement Ḡ is a comparability graph. An f-diagram generalizes the notion of a permulation diagram where the fi are linear functions. It is also shown that G is the intersection graph of the concatenation of ⩽k permutation diagrams if and only if the partial order dimension of Ḡ is ⩽k+1. Computational complexity results are obtained for recognizing such graphs.