
Approximate Graph Spectral Decomposition with the Variational Quantum Eigensolver
Spectral graph theory is a branch of mathematics that studies the relati...
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Just SLaQ When You Approximate: Accurate Spectral Distances for WebScale Graphs
Graph comparison is a fundamental operation in data mining and informati...
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Open problems in the spectral theory of signed graphs
Signed graphs are graphs whose edges get a sign +1 or 1 (the signature)...
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Estimating the Spectral Density of Large Implicit Matrices
Many important problems are characterized by the eigenvalues of a large ...
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Network Summarization with Preserved Spectral Properties
Largescale networks are widely used to represent object relationships i...
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Hitting times and resistance distances of qtriangulation graphs: Accurate results and applications
Graph operations or products, such as triangulation and Kronecker produc...
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Spectra of Perfect State Transfer Hamiltonians on FractalLike Graphs
In this paper we study the spectral features, on fractallike graphs, of...
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Comparing largescale graphs based on quantum probability theory
In this paper, a new measurement to compare two largescale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our proposed distance between two graphs is defined as the distance between the corresponding moment matrices of their spectral distributions. It is shown that the spectral distributions of their adjacency matrices in a vector state includes information not only about their eigenvalues, but also about the corresponding eigenvectors. Moreover, we prove that such distance is graph invariant and substructure invariant. Examples with various graphs are given, and distances between graphs with few vertices are checked. Computational results for real largescale networks show that its accuracy is better than any existing methods and time cost is extensively cheap.
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