Nonextensive Statistical Mechanics

294 7 Thermodynamical and Nonthermodynamical Applications7.8.3 Non-Growing ModelScale-free networks without growth are known since long [865]. We focus here on arecent one [49], on which a q-exponential degree distribution has been numericallyexhibited. See Figs. 7.100, 7.101, and 7.102.Fig. 7.100 A node collapsing (gas-like) model with a merging probability ∝ 1/dij α (α ≥ 0), whered ij is the shortest topological distance between sites i and j on the network. We illustrate here thetime evolution of the number of links of both the most important hub (blue) and of a typical node(red)ofanetworkwithN = 2 7 = 128 nodes and α = 0. In the present model the most linked hubmaintains its “leadership” for ever (Figure following [49].).Fig. 7.101 Cumulative degree distribution of the same model as in Fig. 3 but for α →∞andtypical values of N, where the finite-size effects are visible. Left: log–log scale. Right: The samedata in (q-log) – (linear) scale, for various values of q, the optimal value being q = 1.84 [Inset:The q-dependance of the linear correlation r, which achieves its maximal value (r > 0.9999) forq = 1.84] (Figure following [49].).