Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Ŵk,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥ 1). For each fixed ξ, a fundamental differen...