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We propose a framework for the visualization of directed networks relying onthe eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps.The magnetic Laplacian is a complex deformation of the well-known combinatorialLaplacian. Features such as density of links and directionality patterns arerevealed by plotting the phases of the first magnetic eigenvectors. Aninterpretation of the magnetic eigenvectors is given in connection with theangular synchronization problem. Illustrations of our method are given for bothartificial and real networks.

Magnetic Eigenmaps for the Visualization of Directed Networks