Abstract. Let w(u) be the sum of distances from u to all the other vertices in a graph. The Wiener complexity, C_W(G), is the number of different values w(u) in G, nad the eccentric complexity, C_ec(G), is the number of different eccentricities in G. We prove that for every integer c there are infinitely many graphs G such that C_W(G)-C_ec(G)=c. Moreover, we prove this result using graphs with the smallest possible cyclomatic number. That is if c\ge 0 we prove it using trees, and if c < 0 we prove it using unicyclic graphs. In our proofs we use that w(u) is convex on paths consisting of bridges.