  In order to model entanglements of polymers in a confined region, we consider
the linking numbers and writhes of cycles in random linear embeddings of
complete graphs in a cube. Our main results are that for a random linear
embedding of $K_n$ in a cube, the mean sum of squared linking numbers and the
mean sum of squared writhes are of the order of $\theta(n(n!))$. We obtain a
similar result for the mean sum of squared linking numbers in linear embeddings
of graphs on $n$ vertices, such that for any pair of vertices, the probability
that they are connected by an edge is $p$. We also obtain experimental results
about the distribution of linking numbers for random linear embeddings of these
graphs. Finally, we estimate the probability of specific linking configurations
occurring in random linear embeddings of the graphs $K_6$ and $K_{3,3,1}$.
