  Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs
which are generalizations of Milnor's link-homotopy. We introduce some edge
(resp. vertex)-homotopy invariants of spatial graphs by applying the
Sato-Levine invariant for the 2-component constituent algebraically split links
and show examples of non-splittable spatial graphs up to edge (resp.
vertex)-homotopy, all of whose constituent links are link-homotopically
trivial.

Geometric Topology