  Geometric constraints impact the formation of a broad range of spatial
networks, from amino acid chains folding to proteins structures to rearranging
particle aggregates. How the network of interactions dynamically self-organizes
in such systems is far from fully understood. Here, we analyze a class of
spatial network formation processes by introducing a mapping from geometric to
graph-theoretic constraints. Combining stochastic and mean field analyses
yields an algebraic scaling law for the extent (graph diameter) of the
resulting networks with system size, in contrast to logarithmic scaling known
for networks without constraints. Intriguingly, the exponent falls between that
of self-avoiding random walks and that of space filling arrangements,
consistent with experimentally observed scaling (of the spatial radius of
gyration) for protein tertiary structures.
