  We construct a series of finitely presented semigroups. The centers of these
semigroups encode uniquely up to rigid ambient isotopy in 3-space all
non-oriented spatial graphs. This encoding is obtained by using three-page
embeddings of graphs into the product of the line with the cone on three
points. By exploiting three-page embeddings we introduce the notion of the
three-page complexity for spatial graphs. This complexity satisfies the
properties of finiteness and additivity under natural operations.
