A realization of a graph $G$ in a topological space $X$ is an injective map $\rho:G\to X$ such that $G$ with the graph topology is homeomorphic to $\rho(G)$ with the subspace topology. Of particular interest are realizations of $G$ in 3-dimensional Euclidean space, where each of the edges is a line segment, and where no 4 points of $G$ are coplanar.