  We consider a network of nodes distributed in physical space without physical
links communicating through message broadcasting over specified distances.
Typically, communication using smaller distances is desirable due to savings in
energy or other resources. We introduce a network formation mechanism to enable
reducing the distances while retaining connectivity. Nodes, which initially
transmit signals at a prespecified maximum distance, subject links to
preferential detachment by autonomously decreasing their transmission radii
while satisfying conditions of zero communication loss and fixed maximum
node-hopping distance for signaling. Applied to networks with various spatial
topologies, we find cost reductions as high as 90% over networks that are
restricted to have all nodes with equal transmission distance.
