  We study statistical properties of the highest degree, or most popular, nodes
in growing networks. We show that the number of lead changes increases
logarithmically with network size N, independent of the details of the growth
mechanism. The probability that the first node retains the lead approaches a
finite constant for popularity-driven growth, and decays as N^{-phi}(ln
N)^{-1/2}, with phi=0.08607..., for growth with no popularity bias.
