Magnetic Eigenmaps for the Visualization of Directed Networks

TL;DR

This paper introduces Magnetic Eigenmaps, a novel visualization method for directed networks using eigenfunctions of the magnetic Laplacian, revealing link density and directionality through phase plots.

Contribution

The paper presents a new framework for visualizing directed networks with magnetic Laplacian eigenfunctions, connecting it to angular synchronization.

Findings

Effective visualization of directed networks

Reveals link density and directionality patterns

Applicable to artificial and real networks

Abstract

We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial Laplacian. Features such as density of links and directionality patterns are revealed by plotting the phases of the first magnetic eigenvectors. An interpretation of the magnetic eigenvectors is given in connection with the angular synchronization problem. Illustrations of our method are given for both artificial and real networks.