Network Communities of Dynamical Influence

TL;DR

This paper introduces a method to identify influential nodes and communities in networks by analyzing dominant eigenvectors, revealing insights into rapid consensus, influence distribution, and applications in biological and brain networks.

Contribution

The paper presents a novel eigenvector-based technique for pinpointing key influential nodes and communities in complex networks, enhancing understanding of dynamical influence.

Findings

Starling flock influence linked to low outdegree of birds.

Increasing outgoing connections reduces flock responsiveness.

Method successfully identifies influential communities in brain connectomes.

Abstract

Fuelled by a desire for greater connectivity, networked systems now pervade our society at an unprecedented level that will affect it in ways we do not yet understand. In contrast, nature has already developed efficient networks that can instigate rapid response and consensus, when key elements are stimulated. We present a technique for identifying these key elements by investigating the relationships between a system's most dominant eigenvectors. This approach reveals the most effective vertices for leading a network to rapid consensus when stimulated, as well as the communities that form under their dynamical influence. In applying this technique, the effectiveness of starling flocks was found to be due, in part, to the low outdegree of every bird, where increasing the number of outgoing connections can produce a less responsive flock. A larger outdegree also affects the location of the birds with the most influence, where these influentially connected birds become more centrally located and in a poorer position to observe a predator and, hence, instigate an evasion manoeuvre. Finally, the technique was found to be effective in large voxel-wise brain connectomes where subjects can be identified from their influential communities.