On spectral partitioning of signed graphs
Abstract
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on the Fiedler vector of the standard graph Laplacian for signed graphs. We observe that negative eigenvalues are beneficial for spectral partitioning of signed graphs, making the Fiedler vector easier to compute.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.01394
 Bibcode:
 2017arXiv170101394K
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Machine Learning;
 Mathematics  Numerical Analysis;
 Statistics  Machine Learning;
 05C50;
 05C70;
 15A18;
 58C40;
 65F15;
 65N25;
 62H30;
 91C20;
 H.3.3;
 I.5.3
 EPrint:
 12 pages, 10 figures. Rev 2 to appear in proceedings of the SIAM Workshop on Combinatorial Scientific Computing 2018 (CSC18)