Structural preferential attachment: Stochastic process for the growth of scale-free, modular and self-similar systems

TL;DR

This paper introduces the structural preferential attachment (SPA) model, a stochastic process explaining how complex systems develop scale-free, modular, and self-similar structures, with applications to real-world networks.

Contribution

It provides a detailed analysis of SPA's dynamics, steady-state properties, and introduces approximations for modeling real systems, including the novel peloton dynamics behavior.

Findings

SPA leads to scale-free, modular, self-similar networks

Peloton dynamics predicts features of real growing systems

Analytical and approximation methods for SPA

Abstract

Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behavior and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the modelling of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behavior observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.