Finite size effects in Barabasi-Albert growing networks

TL;DR

This paper analyzes how finite network size affects the degree distribution in Barabasi-Albert models, providing analytical methods to calculate finite size corrections and understanding the influence of initial conditions and multiple links per step.

Contribution

It introduces an analytical spectral moments approach to quantify finite size effects in Barabasi-Albert networks, extending understanding of degree distribution cut-offs.

Findings

Finite size effects depend only on the power-law exponent.

Analytical expressions for finite size corrections are derived.

Initial configuration and multiple links per step influence the degree distribution.

Abstract

We investigate the influence of the network's size on the degree distribution in Barabasi-Albert model of growing network with initial attractiveness. Our approach based on spectral moments allows to treat analytically several variants of the model and to calculate the cut-off function giving finite size corrections to the degree distribution. We study the effect of initial configuration as well as of addition more than one link per time step. The results indicate that asymptotic properties of the cut-off depend only on the exponent in the power law describing the tail of the degree distribution.