  We study the cohomology of complexes of ordinary (non-decorated) graphs,
introduced by M. Kontsevich. We construct spectral sequences converging to zero
whose first page contains the graph cohomology. In particular, these series may
be used to show the existence of an infinite series of previously unknown and
provably non-trivial cohomology classes, and put constraints on the structure
of the graph cohomology as a whole.
