Characterizing the dynamical importance of network nodes and links

TL;DR

This paper introduces a method to quantify the importance of nodes and links in complex networks based on their impact on the largest eigenvalue of the adjacency matrix, with applications to network control.

Contribution

It provides a new quantitative measure of dynamical importance for network nodes and links, considering effects of correlations and community structure.

Findings

Dynamical importance relates to the largest eigenvalue of the adjacency matrix.

Degree correlations and community structure influence importance measures.

Application to real networks demonstrates practical utility.

Abstract

The largest eigenvalue of the adjacency matrix of the networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our characterization of the dynamical importance of nodes can be affected by degree-degree correlations and network community structure. We discuss how our characterization can be used to optimize techniques for controlling certain network dynamical processes and apply our results to real networks.