The Graph Laplacian Matrix
On the Effectiveness of Laplacian Normalization for Graph Semi-supervised Learning
... of graph cut, the ratio cut (Hagen and Kahng, 1992) and the normalized cut (Shi and Malik, ...unnormalized graph Laplacian matrix (which we will define later), and that of the normalized cut ...
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The deformed graph Laplacian and its applications to network centrality analysis
... deformed graph Laplacian, matrix polynomial, nonbacktracking, complex network, generating ...of matrix function ...a matrix polynomial representation, leading to an efficient ...
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Incremental eigenpair computation for graph Laplacian matrices: theory and applications
... a graph Laplacian matrix have been widely used in spectral clustering and community ...the graph Laplacian ...of graph Laplacian matrix to obtain the K-th smallest ...
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The deformed graph Laplacian and its applications to network centrality analysis
... deformed graph Laplacian, matrix polynomial, nonbacktracking, complex network, generating ...of matrix function ...a matrix polynomial representation, leading to an efficient ...
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LAPLACIAN MATRIX IN ALGEBRAIC GRAPH THEORY
... the Laplacian matrix and basis sets of symmetric ...the Laplacian spectral decomposition yield good clusters when MDS or LPP are ...in graph structure can be ...mean graph and its modes ...
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Laplacian energy of a graph
... a graph, pos- sessing n vertices and m ...the graph G, consisting of the numbers λ 1 , λ 2 , ...adjacency matrix [3]. The Laplacian spectrum of the graph G, consisting of the numbers µ ...
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Laplacian Energy of a Fuzzy Graph
... a graph. The spectrum of one such matrix, adjacency matrix is called the spectrum of the ...a graph are related to the properties of the ...of graph theory that deals with this is ...
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Geometric structure of graph Laplacian embeddings
... similarity graph G := {M n , W n } with vertices M n and edge weight matrix W n ...the graph has been constructed a graph Laplacian operator is ...the graph Laplacian are ...
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Affinity Measures Based on the Graph Laplacian
... the graph construction process The graph construction process outlined in Sec- tion 5 is not necessarily the best ...noisy Laplacian matrix makes it even worse because the pseudo inverse ...
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The normalized Laplacian spectrum of subdivisions of a graph
... standard Laplacian matrices of a network behave quite differently [13], and even if the spectrum of one matrix can be determined, it does not mean that the other can also be evaluated unless the ...
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On Eccentricity Version of Laplacian Energy of a Graph
... a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the ...
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Laplacian Sum-Eccentricity Energy of a Graph
... such Laplacian energy, based on the adjacency matrix A, was intro- duced in 2006 [13] and its theory is nowadays elaborated in full detail, see ...this Laplacian energy found interesting engineering ...
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Accelerated Multigrid for Graph Laplacian Operators
... the matrix vector product can be done within linear work in case of sparsity and its stability is guaranteed in the sense that only a moderate amplification of the round-off errors ...coefficient matrix is ...
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On Spectral Properties of the Grounded Laplacian Matrix
... provide graph-theoretic bounds on the smallest eigenvalue based on the number of edges leaving the grounded nodes, bottlenecks in the graph, and properties of the eigenvector associated with the ...grounded ...
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Distance matrix and Laplacian of a tree with attached graphs
... a graph is traditionally defined as the length of a shortest path between the two ...a graph G, the matrix whose (i, j )-entry is the resistance distance between vertices i and j is called the ...
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Graph Controllability Classes for the Laplacian Leader-Follower Dynamics
... the Laplacian Leader-Follower Dynamics Cesar ...ing graph-theoretic characterizations of controllability for the Laplacian-based leader-follower ...of graph controllability classes, namely, ...
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Computing the additive degree-Kirchhoff index with the Laplacian matrix
... undirected graph, it is well known that the Kirchhoff and multiplicative degree–Kirchhoff indices can be computed using the Laplacian ...the Laplacian matrix as the only ...
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The Laplacian Energy of Conjugacy Class Graph of Some Finite Groups
... La graph are the eigenvalues of its Laplacian ...the Laplacian energy of conjugacy class graph of some finite groups and the formulas for the Laplacian energy of conjugacy class ...
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The Network Factor of Equity Pricing: A Signed Graph Laplacian Approach
... the Laplacian matrix and the benefits ...signed Laplacian spectra (the Eigenvalues of the Laplacian matrix) to encode the network structure of the equity market at each time ...The ...
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Quantum Speedup for Graph Sparsification, Cut Approximation and Laplacian Solving
... -cut sparsifier must contain a constant fraction of the edges. As such, the constructed graphs are in fact already sparsifiers. We then carefully “hide” these sparsifiers in a larger, denser graph, in such a way ...
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