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Connecting complex networks to nonadditive entropies

Boltzmann–Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving nonlocal space–time entanglement. Its generalization based on nonadditive q-entropies adequately handles a wide class of such systems.

We show here that scale-invariant networks belong to this class. We numerically study a d-dimensional geographically located network with weighted links and exhibit its ‘energy’ distribution per site at its quasi-stationary state.

Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann–Gibbs exponential factor is generically substituted by its q-generalisation, and is recovered in the q=1q=1 limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.


R. de Oliveira, S. Brito, L. da Silva, C. Tsallis, Connecting complex networks to nonadditive entropies, Scientific Reports 11 (2021) 1130.

Constantino Tsallis, External Faculty at the Complexity Science Hub, celebrates his 80th birthday

Constantino Tsallis

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