Connecting complex networks to nonadditive entropies

Abstract

Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving strong 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 $q=1$ limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

8 pages and 4 figures

References in corpus (20)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Scale-free networks are rare
• Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Thermostatistics of overdamped motion of interacting particles
• Tsallis Fits to pT Spectra and Multiple Hard Scattering in pp Collisions at the LHC
• Experimental validation of nonextensive scaling law in confined granular media
• Preferential attachment growth model and nonextensive statistical mechanics
• Nonextensive aspects of self-organized scale-free gas-like networks
• Statistical properties of the quantum internet
• Role of dimensionality in complex networks: Connection with nonextensive statistics
• Validity and Failure of the Boltzmann Weight
• Nonextensive statistical mechanics and complex scale-free networks
• A generalised model for asymptotically-scale-free geographical networks
• Role of dimensionality in preferential attachment growth in the Bianconi-Barabási model
• Scaling properties of d-dimensional complex networks
• Universal properties of primary and secondary cosmic ray energy spectra

Cited by in corpus (5)

• Approaching a large deviation theory for complex systems
• Statistical mechanical approach of complex networks with weighted links
• Complex network growth model: Possible isomorphism between nonextensive statistical mechanics and random geometry
• Numerical studies for an ab initio investigation into the Boltzmann prescription in statistical mechanics of large systems
• Generalized Algebra Grounded on Nonadditive Entropies