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Unified model for network dynamics exhibiting nonextensive statistics

Stefan Thurner·Fragiskos Kyriakopoulos·Constantino Tsallis
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Abstract

We introduce a dynamical network model which unifies a number of network families which are individually known to exhibit $q$-exponential degree distributions. The present model dynamics incorporates static (non-growing) self-organizing networks, preferentially growing networks, and (preferentially) rewiring networks. Further, it exhibits a natural random graph limit. The proposed model generalizes network dynamics to rewiring and growth modes which depend on internal topology as well as on a metric imposed by the space they are embedded in. In all of the networks emerging from the presented model we find q-exponential degree distributions over a large parameter space. We comment on the parameter dependence of the corresponding entropic index q for the degree distributions, and on the behavior of the clustering coefficients and neighboring connectivity distributions.

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Stefan Thurner, Fragiskos Kyriakopoulos, Constantino Tsallis. 2007-01-02. Unified model for network dynamics exhibiting nonextensive statistics. https://doi.org/10.1103/physreve.76.036111

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