Stochastic model for scale-free networks with cutoffs

TL;DR

This paper introduces a mathematical stochastic model that explains the cutoff behavior in real scale-free networks, providing a theoretical foundation that unifies previous computational models and offers new insights into network growth and aging.

Contribution

The paper presents a novel analytical model that explains cutoff phenomena in scale-free networks, connecting network growth, aging, and equilibrium states.

Findings

Predicts the equilibrium point of active vertices

Relates network growth to aging probability

Unifies existing computational models with a theoretical framework

Abstract

We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We present a mathematical model that can explain several existing computational scale-free network generation models. This yields a theoretical basis to understand cutoff behavior in complex networks, previously treated only with simulations using distinct models. Therefore, ours is an integrative approach that unifies the existing literature on cutoff behavior in scale-free networks. Furthermore, our mathematical model allows us to reach conclusions not hitherto possible with computational models: the ability to predict the equilibrium point of active vertices and to relate the growth of networks with the probability of aging. We also discuss how our model introduces a useful way to classify scale free behavior of complex networks.