Response times of nodes in a complex network environment -- two potential derivation tracks

TL;DR

This paper explores two different analytical methods to derive the scaling exponent linking node response times to network topology in complex systems, demonstrating their consistency across various dynamics.

Contribution

It introduces two derivation tracks for the response time scaling exponent, showing their equivalence despite different functional forms.

Findings

Both derivation methods yield consistent scaling relationships.

The scaling exponent $ heta$ can be derived from nonlinear dynamics.

Predictions hold across diverse types of network dynamics.

Abstract

The spread of perturbative signals in complex networks is governed by the combined effect of the network topology and its intrinsic nonlinear dynamics. Recently, the resulting spreading patterns have been analyzed and predicted, shown to depend on a single scaling relationship, linking a node's weighted degree $S_i$ to its intrinsic response time $\tau_i$. The relevant scaling exponent $\theta$ can be analytically traced to the system's nonlinear dynamics. Here we show that $\theta$ can be obtained via two different derivation tracks, leading to seemingly different functions. Analyzing the resulting predictions, we find that, despite their distinct form, they are fully consistent, predicting the exact same scaling relationship under potentially diverse types of dynamics.