On spectral properties of signed Laplacians for undirected graphs

摘要

Recently, signed weighted graphs have appeared in broad applications, ranging from social networks to biological networks, from distributed control systems to electric power systems. This paper studies the spectral properties of the signed Laplacians associated with undirected signed graphs. We first revisit and provide a new dimension of understanding on the positive semidefiniteness of signed Laplacians via n-port network theory. We then go beyond positive semidefiniteness and characterize the inertia of a signed Laplacian via the notion of the conductance matrix.