  In this paper authors consider representations of graphs in Hilbert spaces
applying a restriction of local scalarity on them. It enables to obtain a
theory, similar to the classical theory of representations of graphs in vector
spaces. In particular, it is obtained a theorem analogous to the well-known
Gabriel theorem: a connected finite graph (wood) is finitely representable in
the category of Hilbert spaces if and only if it is a Dynkin graph.
