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This is a short review article on invariants of spatial graphs, written for A Concise Encyclopedia of Knot Theory (ed. Adams et. al.). The emphasis is on combinatorial and polynomial invariants of spatial graphs, including the Alexander polynomial, the fundamental quandle of a graph, and the Yamada polynomial.
We say that a set of pairs of disjoint cycles $Lambda(G)$ of a graph $G$ is linked if for any spatial embedding $f$ of $G$ there exists an element $lambda$ of $Lambda(G)$ such that the $2$-component link $f(lambda)$ is nonsplittable, and also say min
A {em balanced} spatial graph has an integer weight on each edge, so that the directed sum of the weights at each vertex is zero. We describe the Alexander module and polynomial for balanced spatial graphs (originally due to Kinoshita cite{ki}), and
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood hom
We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration ${mathscr{K}_n(M)}_{ngeq 0}$ of the vector space $mathscr{K}(M)$ spanned by isotopy classes of nullhomologous knots i
C. Giller proposed an invariant of ribbon 2-knots in S^4 based on a type of skein relation for a projection to R^3. In certain cases, this invariant is equal to the Alexander polynomial for the 2-knot. Gillers invariant is, however, a symmetric polyn