  Recently there have been a tremendous interest in models of networks with a
power-law distribution of degree -- so called "scale-free networks." It has
been observed that such networks, normally, have extremely short path-lengths,
scaling logarithmically or slower with system size. As en exotic and
unintuitive example we propose a simple stochastic model capable of generating
scale-free networks with linearly scaling distances. Furthermore, by tuning a
parameter the model undergoes a phase transition to a regime with extremely
short average distances, apparently slower than log log N (which we call a
hypersmall-world regime). We characterize the degree-degree correlation and
clustering properties of this class of networks.
