Recursive weighted treelike networks

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical results indicate that the resulting networks have power-law distributions of degree, strength, weight and betweenness, a scale-free behavior for degree correlations, logarithmic small average path length and diameter with network size. The obtained properties are in agreement with empirical data observed in many real-life networks, which shows that the presented model may provide valuable insight into the real systems. PACS. 89.75.Da Systems obeying scaling laws – 02.10.Ox Combinatorics; graph theory – 89.75.Hc Networks and genealogical trees – 89.20.-a Interdisciplinary applications of physics