Magnetic Eigenmaps for Visualization of Directed Networks

We propose a framework for 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. Directed networks being common in social science, biology or computer science, our visualization method may be relevant for the field of complex networks, as well as applied mathematics and machine learning. Illustrations of our method are given for both artificial and real-life networks.