  We investigate choice-driven network growth. In this model, nodes are added
one by one according to the following procedure: for each addition event a set
of target nodes is selected, each according to linear preferential attachment,
and a new node attaches to the target with the highest degree. Depending on
precise details of the attachment rule, the resulting networks has three
possible outcomes: (i) a non-universal power-law degree distribution; (ii) a
single macroscopic hub (a node whose degree is of the order of N, the number of
network nodes), while the remainder of the nodes comprises a non-universal
power-law degree distribution; (iii) a degree distribution that decays as (k ln
k)^{-2} at the transition between cases (i) and (ii). These properties are
robust when attachment occurs to the highest-degree node from at least two
targets. When attachment is made to a target whose degree is not the highest,
the degree distribution has the ultra-narrow double-exponential form
exp(-const. x e^k), from which the largest degree grows only as ln(ln N).
