  We introduce a novel stochastic growth process, the record-driven growth
process, which originates from the analysis of a class of growing networks in a
universal limiting regime. Nodes are added one by one to a network, each node
possessing a quality. The new incoming node connects to the preexisting node
with best quality, that is, with record value for the quality. The emergent
structure is that of a growing network, where groups are formed around record
nodes (nodes endowed with the best intrinsic qualities). Special emphasis is
put on the statistics of leaders (nodes whose degrees are the largest). The
asymptotic probability for a node to be a leader is equal to the Golomb-Dickman
constant omega=0.624329... which arises in problems of combinatorical nature.
This outcome solves the problem of the determination of the record breaking
rate for the sequence of correlated inter-record intervals. The process
exhibits temporal self-similarity in the late-time regime. Connections with the
statistics of the cycles of random permutations, the statistical properties of
randomly broken intervals, and the Kesten variable are given.
