Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-01-25
Physica A, 376, pp. 692-698 (2007)
Physics
Condensed Matter
Statistical Mechanics
10 pages, 4 figures
Scientific paper
10.1016/j.physa.2006.10.011
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.
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