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

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 ->& nbsp;1 limit of the lambda-state Potts ferromagnet with bond percolation, (ii) the isomorphism, which connects the lambda & RARR; 0 limit of the lambda-state Potts ferromagnet with random resistor networks, and (iii) the de Gennes isomorphism, which connects the n ->& nbsp;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 alpha e q - beta(-epsilon)(q) (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.& nbsp;Published under an exclusive license by AIP Publishing