Generation of scale-free networks using a simple preferential rewiring dynamics

We propose a simple dynamical model that generates networks with power-law degree distributions with the exponent 2 through rewiring only. At each time step, two nodes, i and j, are randomly selected, and one incoming link to i is redirected to j with the rewiring probability R, determined only by degrees of two nodes, k_i and k_j, while giving preference to high-degree nodes. To take the structure of networks into account, we also consider what types of networks are of interest, whether links are directed or not, and how we choose a rewiring link out of all incoming links to i, as a result, specifying 24 different cases of the model. We then observe numerically that networks will evolve to steady states with power-law degree distributions when parameters of the model satisfy certain conditions.