Complex Network Structure of Flocks in the Standard Vicsek Model

TL;DR

This paper analyzes the complex network properties of flocks generated by the Standard Vicsek Model, revealing their high clustering, assortativity, and elevated effective dimensionality, which are linked to their ordered states.

Contribution

It provides the first comprehensive complex network analysis of SVM flocks, uncovering their structural properties and relation to collective order.

Findings

Flocks are highly clustered and assortative networks.

SVM flocks have an effective dimension higher than the embedding space.

Ordered states are sustained even when displacements are suppressed.

Abstract

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.