  The basic functional equations for connected and 2-connnected graphs can be
traced back to the statistical physicists Mayer and Husimi. They play an
essential role in establishing rigorously the virial expansion for imperfect
gases. We survey this approach and inspired by these equations, we investigate
the problem of enumerating some classes of connected graphs all of whose blocks
are contained in a given class B. Included are the species of Husimi graphs (B
= "complete graphs"), cacti (B = "unoriented cycles"), and oriented cacti (B =
"oriented cycles"). For each of these, we consider the question of their
labelled or unlabelled enumeration and of their molecular expansion, according
(or not) to their block-size distributions.
