Detour distance Laplacian matrices for signed networks

Abstract

A signed network [Formula: see text] with the underlying graph [Formula: see text], used as a mathematical model for analyzing social networks, has each edge in [Formula: see text] with a weight [Formula: see text] or [Formula: see text] assigned by the signature function [Formula: see text]. In this paper, we deal with two types of Detour Distance Laplacian (DDL) matrices for signed networks. We characterize balance in signed social networks using these matrices and we compute the DDL spectrum of certain unbalanced signed networks, as balanced signed networks behave like unsigned ones.