Mapping from Architecture to Dynamics: A Unified View of Dynamical Processes on Networks

TL;DR

This paper introduces a universal computational method that maps network topology to emergent dynamical patterns, unifying diverse processes like oscillations and diffusion, and links topological features to complexity and functional diversity.

Contribution

It presents a general transformation linking network structure to dynamics, revealing how topological features influence complexity and evolution of networks.

Findings

Unified framework for diverse dynamical processes

Topological features increase multiscale complexity

Network architecture evolves for functional diversity

Abstract

Although it is unambiguously agreed that structure plays a fundamental role in shaping the dynamics of complex systems, this intricate relationship still remains unclear. We investigate a general computational transformation by which we can map the network topology directly to the dynamical patterns emergent on it -- independent of the nature of the dynamical process. We find that many seemingly diverse dynamical processes such as coupled oscillators and diffusion phenomena can all be understood and unified through this same procedure. Using the multiscale complexity measure derived form the structure-dynamics transformation, we find that the topological features like hierarchy, heterogeneity and modularity all result in higher complexity. This result suggests a universal principle: it is the desire for functional diversity that drives the evolution of network architecture.