  We introduce a simple network model that is inspired by social information
networks such as twitter. Agents are nodes, connecting to another agent by
building a directed edge has a cost, and reaching other agents via short
directed paths has a benefit; in effect, an agent wants to reach others
quickly, but without the cost of directly connecting each and every one. Even
in its simplest form, edges in this framework are neither substitutes or
complements in general; hence, standard techniques are required to study the
model's properties and dynamics do not apply.
  We prove that an asynchronous edge dynamics always converge to a stable
network; in fact, for this convergence is fast for a range of parameters.
Moreover, the set of stable networks are nontrivial and can support the type of
network structures that have been observed to appear in social information
networks -- from community clusters to broadcast networks, depending on the
parameters many natural formations can emerge. We further study the static
game, and give classes of stable and efficient networks for nontrivial
parameter ranges. We close several problems, and leave many interesting ones
open.
