Network evolution towards optimal dynamical performance

TL;DR

This paper introduces a generic method to evolve network structures to optimize dynamical performance, demonstrated through diffusion processes modeled by the graph Laplacian, revealing insights into the interplay between network topology and dynamics.

Contribution

The paper presents a novel, spectrum-based network evolution approach applicable to various dynamics, enabling targeted structural modifications for desired dynamical behaviors.

Findings

Networks can be evolved to exhibit specific dynamical properties.

The spectrum-based evolution method is versatile across different dynamics.

Evolved networks show improved or targeted performance in diffusion processes.

Abstract

Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this relationship which is applicable to a wide class of dynamics, namely to evolve networks using a performance measure based on the whole spectrum of the dynamics' time evolution operator. As an example, we consider the graph Laplacian describing diffusion processes, and we evolve the network structure such that a given sub-diffusive behavior emerges.