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Magnetic Eigenmaps for the Visualization of Directed Networks

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arxiv 1606.08266 v2 pith:ZVTXLKFP submitted 2016-06-27 cs.SI physics.soc-ph

Magnetic Eigenmaps for the Visualization of Directed Networks

Micha\"el Fanuel , Carlos M. Ala\'iz , \'Angela Fern\'andez , Johan A. K. Suykens This is my paper
classification cs.SI physics.soc-ph
keywords magneticlaplaciannetworksdirectedeigenmapseigenvectorsgivenvisualization
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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.

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