A measure of individual role in collective dynamics

TL;DR

This paper introduces a dynamical influence measure that quantifies how individual nodes affect collective behavior in complex systems, considering both network structure and dynamics, improving identification of key players.

Contribution

It proposes a new measure of dynamical influence that captures the interplay between network structure and dynamics, advancing the identification of influential nodes in collective systems.

Findings

Dynamical influence correlates with spreading capabilities.

It effectively identifies key nodes in diffusive processes.

The measure improves control strategies in complex networks.

Abstract

Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single out the role of individual elements in such intermingled systems, or which is the best way to quantify their importance. Centrality measures describe a node's importance by its position in a network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely determined by the structure of the system but it is a result of the interplay between dynamics and network structure. We show that dynamical influence measures explicitly how strongly a node's dynamical state affects collective behavior. For critical spreading, dynamical influence targets nodes according to their spreading capabilities. For diffusive processes it quantifies how efficiently real systems may be controlled by manipulating a single node.