From regular lattice to scale free network - yet another algorithm

The Watts-Strogatz algorithm transferring a regular lattice to the small world network is modified by introducing preferential rewiring constrained by connectivity demand. The probability to link to/ unlink form a node is dependent on a vertex degree and adjusted by some threshold. For each threshold value there exists a probability at which the resulting stationary network has degree distribution with power-law decay in large interval of degrees.