  Approaches from statistical physics are applied to investigate the structure
of network models whose growth rules mimic aspects of the evolution of the
world-wide web. We first determine the degree distribution of a growing network
in which nodes are introduced one at a time and attach to an earlier node of
degree k with rate A_ksim k^gamma. Very different behaviors arise for gamma<1,
gamma=1, and gamma>1. We also analyze the degree distribution of a
heterogeneous network, the joint age-degree distribution, the correlation
between degrees of neighboring nodes, as well as global network properties. An
extension to directed networks is then presented. By tuning model parameters to
reasonable values, we obtain distinct power-law forms for the in-degree and
out-degree distributions with exponents that are in good agreement with current
data for the web. Finally, a general growth process with independent
introduction of nodes and links is investigated. This leads to independently
growing sub-networks that may coalesce with other sub-networks. General results
for both the size distribution of sub-networks and the degree distribution are
obtained.
