Complex network growth model: Possible isomorphism between nonextensive statistical mechanics and random geometry

Abstract

In the realm of Boltzmann-Gibbs statistical mechanics there are three well known isomorphic connections with random geometry, namely (i) the Kasteleyn-Fortuin theorem which connects the $\lambda \to 1$ limit of the $\lambda$-state Potts ferromagnet with bond percolation, (ii) the isomorphism which connects the $\lambda \to 0$ limit of the $\lambda$-state Potts ferromagnet with random resistor networks, and (iii) the de Gennes isomorphism which connects the $n\to 0$ limit of the $n$-vector ferromagnet with self-avoiding random walk in linear polymers. We provide here strong numerical evidence that a similar isomorphism appears to emerge connecting the energy $q$-exponential distribution $\propto e_q^{-{\beta }_q\epsilon }$ (with $q=4/3$ and ${\beta }_q{\omega }_0=10/3$) optimizing, under simple constraints, the nonadditive entropy $S_q$ with a specific geographic growth random model based on preferential attachment through exponentially-distributed weighted links, ${\omega }_0$ being the characteristic weight.

5 pages and 2 figures

References in corpus (1)

• Connecting complex networks to nonadditive entropies