  A univariate graph polynomial P(G;X) is weakly distinguishing if for almost
all finite graphs G there is a finite graph H with P(G;X)=P(H;X). We show that
the clique polynomial and the independence polynomial are weakly
distinguishing. Furthermore, we show that generating functions of induced
subgraphs with property C are weakly distinguishing provided that C is of
bounded degeneracy or tree-width. The same holds for the harmonious chromatic
polynomial.
