Fluctuations in network dynamics

TL;DR

This paper investigates how flux fluctuations in different networks relate to their total activity, revealing a universal scaling law that links internal dynamics and external influences, with implications for predicting network behavior.

Contribution

It introduces a new scaling law connecting flux fluctuations to total flux in various networks, explaining the interplay between internal and external dynamics.

Findings

Flux fluctuations follow a unique scaling law in each network.

The scaling law explains the balance between internal dynamics and external changes.

Predictions of scaling exponents match observed data across networks.

Abstract

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding that for each the coupling of the flux fluctuations with the total flux on individual nodes obeys a unique scaling law. We show that the observed scaling can explain the competition between the system's internal collective dynamics and changes in the external environment, allowing us to predict the relevant scaling exponents.