Rute Oliveira, Luciano R. da Silva, Constantino Tsallis
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Energy distribution in long-range-interacting weighted geographic networks
We numerically investigate a geographical d-dimensional (\(d=1,2,3,4\)) Bianconi–Barabási-like model, characterized by preferential attachment growth mechanisms influenced by Euclidean distances and weighted edges. The weights of the edges follow a predetermined random probability distribution. This model is implemented through a straightforward energy-driven dynamics and exhibits the distribution of ’energy’ per site in its quasi-stationary state. Across all networks generated by this model, we observe q-exponential energy distributions over the entire parameter space, which exhibits that this model belongs to the realm of nonadditive q-entropies. Additionally, the time evolution of the site energies, characterized by the dynamic \(\beta _{\varepsilon }-\)exponent, is analyzed.
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