Nonextensive aspects of self-organized scale-free gas-like networks

TL;DR

This paper models a self-organized scale-free network as a gas-like system, demonstrating nonextensive statistical behavior in degree distribution influenced by interaction potential decay.

Contribution

It introduces a gas-like dynamical model for scale-free networks incorporating nonextensive statistics and analyzes how interaction potential affects degree distribution.

Findings

System exhibits nonextensive degree distribution

Entropic index q varies with decay parameter alpha

Recovers Kim et al.'s models at alpha=0 and infinity

Abstract

We explore the possibility to interpret as a 'gas' the dynamical self-organized scale-free network recently introduced by Kim et al (2005). The role of 'momentum' of individual nodes is played by the degree of the node, the 'configuration space' (metric defining distance between nodes) being determined by the dynamically evolving adjacency matrix. In a constant-size network process, 'inelastic' interactions occur between pairs of nodes, which are realized by the merger of a pair of two nodes into one. The resulting node possesses the union of all links of the previously separate nodes. We consider chemostat conditions, i.e., for each merger there will be a newly created node which is then linked to the existing network randomly. We also introduce an interaction 'potential' (node-merging probability) which decays with distance d_ij as 1/d_ij^alpha; alpha >= 0). We numerically exhibit that this system exhibits nonextensive statistics in the degree distribution, and calculate how the entropic index q depends on alpha. The particular cases alpha=0 and alpha to infinity recover the two models introduced by Kim et al.