Normalized graph Laplacians for directed graphs

By Frank Bauer. 2011

77 citations recorded by the source corpus.

We consider the normalized Laplace operator for directed graphs with positive and negative edge weights. This generalization of the normalized Laplace operator for undirected graphs is used to characterize directed acyclic graphs. Moreover, we identify certain structural properties of the underlying graph with extremal eigenvalues of the normalized Laplace operator. We prove comparison theorems that establish a relationship between the eigenvalues of directed graphs and certain undirected graphs. This relationship is used to derive eigenvalue estimates for directed graphs. Finally we introduce the concept of neighborhood graphs for directed graphs and use it to obtain further eigenvalue estimates.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0bcbcfcab1e99cbc0b17c30e3bc692ce55f0f87a

How researchers see this paper

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

In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “to introduce definitions appropriate for directed graphs as well [89], [90].”
Hypergraph Laplace operators for chemical reaction networks (2018, background): “s educts or inputs, to another collection, its products or outputs. We could therefore deﬁne a suitable Laplace type operator for a directed hypergraph and study its spectrum, as pioneered by F.Bauer [2] for directed graphs. Since such an operator is not self-adjoint w.r.t. some scalar product, howe”