On the spectrum of the normalized graph Laplacian

By Anirban Banerjee, Jürgen Jost. 2007

123 citations recorded by the source corpus.

We investigate how the spectrum of the normalized (geometric) graph Laplacian is affected by operations like motif dougling, graph splitting or joining. The multiplicity of the eigenvalue 1, or equivalently, the dimension of the kernel of the adjacency matrix of the graph is of particular interest. This multiplicity can be increased, for instance, by motif doubling.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/27ebbed04bbab7213aae1068c3c09b0c2a677ad7

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

1. Jürgen Jost
2. Raffaella Mulas
3. S. Butler
4. Frank Bauer
5. Danijela Horak
6. Anirban Banerjee
7. Lorenzo Rosasco

In Geometry and Topology

1. Jürgen Jost
2. Raffaella Mulas
3. Frank Bauer
4. S. Butler
5. Danijela Horak
6. Anirban Banerjee
7. Florentin Münch

In Organic Chemistry

1. Raffaella Mulas
2. Jürgen Jost
3. S. Butler
4. Danijela Horak
5. Anirban Banerjee

Citations in the corpus

• Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplacian (2009, background): “by h[1] = 1 1+c , h[2] = 2c (1+c)2 , h[3] = 3c2+1 (1+c)3 , h[4] = 4c3+4c (1+c)4 , and h[5] = 1+10c2+c4 (1+c)5 .”
• On the spectrum of hypergraphs (2017, background): “Eigenvalues of the transition probability operator can be estimated from the spectrum of normalized graph Laplacian [3].”
• Spectra of combinatorial Laplace operators on simplicial complexes (2011, background): “This theorem is a generalization of the vertex doubling effect on the normalized graph Laplacian ∆ 0 discussed in [2].”
• Hypergraph Laplace operators for chemical reaction networks (2018, methodology): “The definition of minimal closed system of reactions makes sense since it is easy to see that: (1) S, S ′ closed systems =⇒ S ∪ S ′ closed system; (2) S, S ′ closed systems with S ( S ′ =⇒ S ′ \ S closed system.”
• Algebraic aspects of the normalized Laplacian (2016, background): “The idea of twin subgraphs has appeared in the work of Banarjee and Jost [1] and Banarjee and Mehatari [2].”