K e y w o r d s G r a p h drawing, Laplaclan, Eigenvectors, Fledler vector, Force-directed layout, Spectral graph theory 1. I N T R O D U C T I O N A graph G(V, E) is an abstract structure that is used to model a relation E over a set V of entities. Graph drawing is a standard means for visualizing relational information, and its ultimate usefulness depends on the readability of the resulting l...

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.

Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory robust theory. By challenging the classical Laplacian, propose a new convolution operator that is provably in domain and incorporated GCN architecture improve expressiv...

We review the recently developed method for spectral analysis of growing graphs on the basis of quantum (or noncommutative or algebraic) probability theory. The asymptotic spectral distribution of a growing regular graph is derived from the quantum central limit theorem for quantum components of the adjacency matrix. Mathematics Subject Classifications (2000): Primary 46L53; Secondary 05C50, 42...

6 Spectral Graph Theory 16 6.1 Graph Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.2 Polynomial interlacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.2.1 An Application to Expander Graphs . . . . . . . . . . . . . . . . . . 18 6.3 Connectivity as a Minimization Problem . . . . . . . . . . . . . . . . . . . . 20 6.4 Courant-Fisher and Alg...

We give a new proof that there exists a unique strongly regular graph with parameters (81, 20, 1, 6). Unlike the finite geometry approach used by Brouwer and Haemers, we use linear algebra and spectral graph theory concepts, namely the technique of star complements, in our proof. AMS Classification: 05E30, 05C50

In this book chapter we address the problem of 3D shape registration and we propose a novel technique based on spectral graph theory and probabilistic matching. Recent advancement in shape acquisition technology has led to the capture of large amounts of 3D data. Existing real-time multi-camera 3D acquisition methods provide a frame-wise reliable visual-hull or mesh representations for real 3D ...

Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbor nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constra...