Microdynamics in stationary complex networks

TL;DR

This paper investigates the microscopic dynamics of the US airport network over a decade, revealing intense local fluctuations and broad link lifetime distributions, and proposes a model capturing these observed behaviors.

Contribution

It provides the first detailed empirical analysis of microscopic link dynamics in a large-scale real-world network and introduces a model reproducing these dynamics.

Findings

Links have broad lifetime distributions.

Links connecting airports with different traffic are highly volatile.

The proposed model replicates empirical statistical and dynamical properties.

Abstract

Many complex systems, including networks, are not static but can display strong fluctuations at various time scales. Characterizing the dynamics in complex networks is thus of the utmost importance in the understanding of these networks and of the dynamical processes taking place on them. In this article, we study the example of the US airport network in the time period 1990-2000. We show that even if the statistical distributions of most indicators are stationary, an intense activity takes place at the local (`microscopic') level, with many disappearing/appearing connections (links) between airports. We find that connections have a very broad distribution of lifetimes, and we introduce a set of metrics to characterize the links' dynamics. We observe in particular that the links which disappear have essentially the same properties as the ones which appear, and that links which connect airports with very different traffic are very volatile. Motivated by this empirical study, we propose a model of dynamical networks, inspired from previous studies on firm growth, which reproduces most of the empirical observations both for the stationary statistical distributions and for the dynamical properties.