The condensation in non-growing complex networks under Boltzmann limit

TL;DR

This paper extends the Bianconi-Barabási fitness model to fixed-size non-growing networks, analyzing phase transitions and deviations from power-law degree distributions using numerical simulations.

Contribution

It introduces a non-growing network model based on Boltzmann statistics and characterizes its phase transition and connectivity properties.

Findings

Identification of a critical temperature $T_c$ for phase transition.

The non-condensation phase differs from the fit-get-rich phase.

Degree distribution deviates from power-law at various temperatures.

Abstract

We extend the Bianconi-Barab\'asi (B-B) fitness model to the non-growing complex network with fixed number of nodes and links. It is found that the statistical physics of this model makes it an appropriate representation of the Boltzmann statistics in the context of complex networks. The phase transition of this extended model is illustrated with numerical simulation and the corresponding "critical temperature" $T_c$ is identified. We note that the "non-condensation phase" in $T > T_c$ regime is different with "fit-get-rich" (FGR) phase of B-B model and that the connectivity degree distribution P(k) deviates from power-law distribution at given temperatures.