Magnetic Eigenmaps for the visualization of directed networks |
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Authors: | Michaël Fanuel Carlos M Alaíz Ángela Fernández Johan AK Suykens |
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Institution: | KU Leuven, Department of Electrical Engineering (ESAT), Kasteelpark Arenberg 10, B-3001 Leuven, Belgium |
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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. |
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Keywords: | Magnetic Eigenmaps Magnetic Laplacian Directed graph Data visualization |
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