In this paper we prove that the homology of the complex of 2-connected
graphs is naturally isomorphic to the homology of the graph-complex of
trees.
Both complexes are connected with  combinatorics of  knot spaces.
More precisely the first complex appears in the spectral approach to the 
calculation of the homology of the space of knots in ${\bf R}^n$, $n\ge 3$ 
(see~[V2, V4]). The homology of the second complex has a natural 
interpretation in the bialgebra of Chinese diagrams (see~[BN]). 
This bialgebra turned out to be a very useful tool in the investigation 
of the space of finite order knot invariants. The isomorphism in question 
provides a connection between the two mentioned approaches.