Sparsification of the regularized magnetic Laplacian with multi-type spanning forests

arXiv:2208.14797v2 Announce Type: replace-cross
Abstract: In this paper, we consider a ${\rm U}(1)$-connection graph, that is, a graph where each oriented edge is endowed with a unit modulus complex number that is conjugated under orientation flip. A natural replacement for the combinatorial Laplacian is then the magnetic Laplacian, an Hermitian matrix that includes information about the graph's connection. Magnetic Laplacians appear, e.g., in the problem of angular synchronization. In the context of large and dense graphs, we study here sparsifiers …

abstract arxiv cs.lg cs.si edge forests graph modulus natural paper replacement stat.ml type