Spectral partitioning of signed graphs by repulsion

My paper "On spectral partitioning of signed graphs" from https://arxiv.org/abs/1701.01394 has appeared in proceedings of the SIAM Workshop on Combinatorial Scientific Computing 2018 (CSC18); see https://epubs.siam.org/doi/abs/10.1137/1.9781611975215.2 It has been patent-pending, see https://patents.google.com/patent/US20150363361, but no longer, so open for the community to freely use!

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 Fielder 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.