Eigenvalues of the Laplacian of a graph

By W. Anderson, D. Thomas, Morley, TR 71-U. 1985

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Citations in the corpus

A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, methodology): “, [78], [96], [97], [102]) overcome this problem by first constructing a k nearest neighbour (KNN) graph from the data feature.”
Spectra of Graphs (2011, background): “55 36 45 1(65) −10(12) ! 81 16 7 2 7(16) −2(64) 9(2); from a partial spread: projective ternary [8,4] code with weights 3, 6 64 49 56 1(64) −8(16) OA(9,8) ! 81 20 1 6 2(60) −7(20) unique by Brouwer & Haemers [65]; V O 4 (3) affine polar graph; projective ternary [10,4] code with weights 6, 9 60 45 4”
Group-Wise Learning for Aurora Image Classification With Multiple Representations (2019, background): “It is worth noting that an edge in a graph connects two vertices, through which pairwise relationship among samples can be modeled explicitly [30], [31], [46], [54].”
Dimensionality Reduction: A Comparative Review (2008, methodology): “The computation of the degree matrix M and the graph Laplacian L of the graph W allows for formulating the minimization problem as an eigenproblem [4].”
On the spectra of nonsymmetric Laplacian matrices (2005, background): “ deﬁnition, Le(Γ) = (nb)−1L(Γ). It follows from [1, Theorem 1] (or from the earlier results (2.7) and (2.10) of [16]) that, in the case of symmetric Laplacian matrices, the eigenvalues of Lebelong to [0,1]. In the general case, (4), (6), and Gerˇsgorin’s theorem immediately provide 1Studying the spe”
Spectra of combinatorial Laplace operators on simplicial complexes (2011, background): “This is the well-known bound on the maximal eigenvalue of L 0 (see [1]).”
Bounding the largest eigenvalue of trees in terms of the largest vertex degree (2003, background): “It is well known that if G ∈ G∆ then √ ∆ ≤ λ1(G) ≤ ∆ (1)”
Isoperimetric graph partitioning for image segmentation (2006, background): “Anderson and Morley [23] proved that the spectral radius of L, ρ(L), satisfies ρ(L) ≤ 2dmax, suggesting that grounding the node of highest degree may have the most beneficial effect on the conditioning of (13).”
Consensus in multi-agent systems: a review (2021, methodology): “The neighborhood matrix of A = [ a ij ] ∈ R n × n for graph G = ( V , E ) is defined as (Anderson and Morley 1985): By using Eq.”
Shifted simplicial complexes are Laplacian integral (2002, background): “The spectra of graph Laplacians gained attention in the late 1960s through the independent work of Anderson and Morley [ 2 ], Fiedler [13], and Kelmans (see references in [20]).”
On the spectral radius of graphs (2004, background): “with equality if and only if the graph is empty. Lemma 3 [ 1 ].”
de Caen's inequality and bounds on the largest Laplacian eigenvalue of a graph (2001, background): “Anderson and Morley [1] proved that λ1(G) max{di + dj : vivj ∈ E(G)}.”
Graph Embedding and Dimensionality Reduction - A Survey (2013, background): “Laplacian Eigenmaps uses spectral techniques to perform dimensionality reduction.”