Generalized inverse of the Laplacian matrix and some applications

By Ivan Gutman, W. Xiao. 2004

153 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Kron Reduction of Graphs With Applications to Electrical Networks (2011, unknown): “We refer the reader to [10], [16], [38]–[41] for various applications and properties of the effective resistance as well as interesting results relating , , , , and .”
netmeta: An R Package for Network Meta-Analysis Using Frequentist Methods (2023, unknown): “However, its Moore-Penrose pseudoinverse L + (Rao and Mitra 1971; Gutman and Xiao 2004) is deﬁned and can be calculated by where J is a n × n matrix whose elements are all 1.”
Network meta‐analysis, electrical networks and graph theory (2012, methodology): “We define the n n Laplacian matrix L by L ¼ B>WB: (2) The Laplacian matrix (also called Kirchhoff or admittance matrix) plays a central role in spectral graph theory (Rao and Mitra, 1971; Doyle and Snell, 1999; Bollobás, 2002; Spielman and Srivastava, 2009; Spielman, 2012).”
A tutorial on spectral clustering (2007, methodology): “For further properties of L† see Gutman and Xiao (2004). Proposition 6 (Commute distance) Let G = (V,E) a connected, undirected graph. Denote by cij the commute distance between vertex vi and vertex vj, and by L† = (l † ij)i,j=1,...,n the generalized inverse of L. Then we have: cij = vol(V )(l † ii ”