Finite-time fluctuations in the degree statistics of growing networks

TL;DR

This paper analyzes finite-time fluctuations in the degree distributions of various growing network models, revealing different behaviors across regimes and providing insights into finite-size effects.

Contribution

It offers a detailed finite-time analysis of degree statistics in several growing network models, including uniform, linear, and generalized preferential attachment.

Findings

Finite-size effects vary across stationary, scaling, and large deviation regimes.

Different models exhibit distinct finite-time fluctuation behaviors.

The study enhances understanding of network growth dynamics at finite sizes.

Abstract

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barab\'asi-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.