Spectral Graph Theory

Bekas, Costas; Curioni, A.; Arbenz, Peter; Flaig, Cyril; Lenthe, G. Harry van; ̈ller, R. Mu; Wirth, Andreas

doi:10.1201/b11644-19

Cited by 174 publications

(179 citation statements)

References 74 publications

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“…Spectral graph theory can be defined as the study and analysis of the graph topology using the eigenvalues and eigenvectors of matrices associated with those graphs (Spielman, 2009). The first applications of the spectral graph theory originated in quantum chemistry to study organic molecular structures.…”

Section: Spectral Graph Theorymentioning

confidence: 99%

A novel 2D shape signature method based on complex network spectrum

Oliveira

Silva

Barone

2015

Pattern Recognition Letters

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Section: Spectral Graph Theorymentioning

confidence: 99%

A novel 2D shape signature method based on complex network spectrum

Oliveira

Silva

Barone

2015

Pattern Recognition Letters

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“…Based on the above preparation, we define the Laplacian matrix L of directed graph G(V, E) as follows [4], [5] (Fig. 1).…”

Section: Definition Of the Laplacian Matrixmentioning

confidence: 99%

“…, m n ) means the scaling factors of nodes. That is, we define a directed graph as symmetrizable iff all its links satisfy (5). Figure 3 shows a simple example of the procedure that leads to (8).…”

Section: Symmetrization Of Laplacian Matrix and The Scaled Laplacian mentioning

confidence: 99%

Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction

Aida

Takano

Murata

2018

IEICE Trans. Commun.

115

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SUMMARYThis paper proposes an oscillation model for analyzing the dynamics of activity propagation across social media networks. In order to analyze such dynamics, we generally need to model asymmetric interactions between nodes. In matrix-based network models, asymmetric interaction is frequently modeled by a directed graph expressed as an asymmetric matrix. Unfortunately, the dynamics of an asymmetric matrix-based model is difficult to analyze. This paper, first of all, discusses a symmetric matrix-based model that can describe some types of link asymmetry, and then proposes an oscillation model on networks. Next, the proposed oscillation model is generalized to arbitrary link asymmetry. We describe the outlines of four important research topics derived from the proposed oscillation model. First, we show that the oscillation energy of each node gives a generalized notion of node centrality. Second, we introduce a framework that uses resonance to estimate the natural frequency of networks. Natural frequency is important information for recognizing network structure. Third, by generalizing the oscillation model on directed networks, we create a dynamical model that can describe flaming on social media networks. Finally, we show the fundamental equation of oscillation on networks, which provides an important breakthrough for generalizing the spectral graph theory applicable to directed graphs.

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“…We have designed in [12], [13] new coupling-strength allocation methods for undirected networks using recently reported tools in spectral graph theory [14]. The idea of graph comparison [14], [15] turns out to be especially useful.…”

Section: Introductionmentioning

confidence: 99%

“…The idea of graph comparison [14], [15] turns out to be especially useful. In this paper, we further develop our methodologies by looking at general directed networks.…”

Section: Introductionmentioning

confidence: 99%

Synchronization in Directed Complex Networks Using Graph Comparison Tools

Liu

Cao

Wu³

et al. 2015

IEEE Trans. Circuits Syst. I

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This paper proposes lower bounds for the coupling strengths of oscillators in directed networks to guarantee global synchronization. The novel idea of graph comparison from spectral graph theory is employed so that the combinatorial features of a given network can be fully utilized to simplify computations. For large networks that can be decomposed into a set of smaller strongly connected components, the comparison can be carried out at the local level as well. To validate theoretical analysis, examples are provided to demonstrate how to apply the proposed methodologies to typical directed complex networks. . Her main research interests are complex networks, cooperative control of networked systems, nonlinear control systems, network modeling and computation, and graph theory.Ming Cao (S'02-M'08) is currently an associate professor and chair of the research unit on network analysis and control with the Faculty of Mathematics and Natural Sciences at

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Spectral Graph Theory

Cited by 174 publications

References 74 publications

A novel 2D shape signature method based on complex network spectrum

A novel 2D shape signature method based on complex network spectrum

Oscillation Model for Describing Network Dynamics Caused by Asymmetric Node Interaction

Synchronization in Directed Complex Networks Using Graph Comparison Tools

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