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

  title={Complex network growth model: Possible isomorphism between nonextensive statistical mechanics and random geometry.},
  author={Constantino Tsallis and Rute Oliveira},
  volume={32 5},
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 λ → 1 limit of the λ-state Potts ferromagnet with bond percolation, (ii) the isomorphism, which connects the λ → 0 limit of the λ-state Potts ferromagnet with random resistor networks, and (iii) the de Gennes isomorphism, which connects the n → 0 limit of the n-vector ferromagnet with self-avoiding random… 

Figures from this paper



Role of dimensionality in complex networks

D-dimensional geographically-located networks which grow with preferential attachment involving Euclidean distances through q-statistics are introduced and it is numerically verified that the q-exponential degree distributions exhibit universal dependences on the ratio αA/d.

Statistical mechanics of complex networks

A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.

Connecting complex networks to nonadditive entropies

The Boltzmann–Gibbs exponential factor is generically substituted by its q -generalisation, and is recovered in the $$q=1$$ q = 1 limit when the nonlocal effects fade away.

Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere

The present review focuses on nonadditive entropies generalizing Boltzmann–Gibbs statistical mechanics and their predictions, verifications, and applications in physics and elsewhere.

Emergence of scaling in random networks

A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

The self-avoiding walk

The self-avoiding walk is a mathematical model with important applications in statistical mechanics and polymer science. This text provides a unified account of the rigorous results for the

Possible generalization of Boltzmann-Gibbs statistics

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelySq ≡k [1 – ∑i=1W piq]/(q-1), whereq∈ℝ characterizes the generalization andpi are the

Break-collapse method for resistor networks and a renormalisation-group application

The break-collapse method recently introduced for the q-state Potts model is adapted for resistor networks. This method greatly simplifies the calculation of the conductance of an arbitrary