  We show that large subsets of vector spaces over finite fields determine
certain point configurations with prescribed distance structure. More
specifically, we consider the complete graph with vertices as the points of $A
\subseteq \mathbf{F}_q^d$ and edges assigned the algebraic distance between
pairs of vertices. We prove nontrivial results on locating specified subgraphs
of maximum vertex degree at most $t$ in dimensions $d \geq 2t$.
