  Let $G$ be a simple graph with binomial edge ideal $J_G$. We prove how to
calculate the multidegree of $J_G$ based on combinatorial properties of $G$. In
particular, we study the set $S_{\min}(G)$ defined as the collection of subsets
of vertices whose prime ideals have minimum codimension. We provide results
which assist in determining $S_{\min}(G)$, then calculate $S_{\min}(G)$ for
star, horned complete, barbell, cycle, wheel, and friendship graphs, and use
the main result of the paper to obtain the multidegrees of their binomial edge
ideals.
