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Relevant bibliographies by topics / Normalized laplacian matrix

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Academic literature on the topic 'Normalized laplacian matrix'

Author: Grafiati

Published: 4 June 2025

Last updated: 6 July 2025

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Journal articles on the topic "Normalized laplacian matrix"

1

Reinhart, Carolyn. "The normalized distance Laplacian." Special Matrices 9, no. 1 (2021): 1–18. http://dx.doi.org/10.1515/spma-2020-0114.

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Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

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Yu, Guihai, and Hui Qu. "More on Spectral Analysis of Signed Networks." Complexity 2018 (October 16, 2018): 1–6. http://dx.doi.org/10.1155/2018/3467158.

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Spectral graph theory plays a key role in analyzing the structure of social (signed) networks. In this paper we continue to study some properties of (normalized) Laplacian matrix of signed networks. Sufficient and necessary conditions for the singularity of Laplacian matrix are given. We determine the correspondence between the balance of signed network and the singularity of its Laplacian matrix. An expression of the determinant of Laplacian matrix is present. The symmetry about 1 of eigenvalues of normalized Laplacian matrix is discussed. We determine that the integer 2 is an eigenvalue of normalized Laplacian matrix if and only if the signed network is balanced and bipartite. Finally an expression of the coefficient of normalized Laplacian characteristic polynomial is present.

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3

El Seidy, Essam, Salah Eldin Hussein, and Atef Mohamed. "Properties of the characteristic polynomials and spectrum of Pn and Cn." International Journal of Applied Mathematical Research 5, no. 2 (2016): 132. http://dx.doi.org/10.14419/ijamr.v5i2.6106.

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We consider a finite undirected and connected simple graph with vertex set and edge set .We calculated the general formulas of the spectra of a cycle graph and path graph. In this discussion we are interested in the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, and seidel adjacency matrix.

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4

Yu, Guihai, Matthias Dehmer, Frank Emmert-Streib, and Herbert Jodlbauer. "Hermitian normalized Laplacian matrix for directed networks." Information Sciences 495 (August 2019): 175–84. http://dx.doi.org/10.1016/j.ins.2019.04.049.

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5

Lorenzen, Kate. "Cospectral constructions for several graph matrices using cousin vertices." Special Matrices 10, no. 1 (2021): 9–22. http://dx.doi.org/10.1515/spma-2020-0143.

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Abstract Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us establish patterns about structural information not preserved by the spectrum. We generalize a construction for cospectral graphs previously given for the distance Laplacian matrix to a larger family of graphs. In addition, we show that with appropriate assumptions this generalized construction extends to the adjacency matrix, combinatorial Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, and distance matrix. We conclude by enumerating the prevelance of this construction in small graphs for the adjacency matrix, combinatorial Laplacian matrix, and distance Laplacian matrix.

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6

Usha, Subramaniam, Murugesan Karthik, Marappan Jothibasu, and Vijayaragavan Gowtham. "An integrated exploration of heat kernel invariant feature and manifolding technique for 3D object recognition system." Acta Scientiarum. Technology 46, no. 1 (2023): e62608. http://dx.doi.org/10.4025/actascitechnol.v46i1.62608.

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Spectral Graph theory has been utilized frequently in the field of Computer Vision and Pattern Recognition to address challenges in the field of Image Segmentation and Image Classification. In the proposed method, for classification techniques, the associated graph's Eigen values and Eigen vectors of the adjacency matrix or Laplacian matrix created from the images are employed. The Laplacian spectrum and a graph's heat kernel are inextricably linked. Exponentiating the Laplacian eigensystem over time yields the heat kernel, which is the solution to the heat equations. In the proposed technique K-Nearest neighborhood and Delaunay triangulation techniques are used to generate a graph from the 3D model. The graph is then represented into Normalized Laplacian (NL) and Laplacian matrix (L). From each Normalized Laplacian and Laplacian matrix, the feature vectors like Heat Content Invariant and Laplacian Eigen values are extracted. Then, using all of the available clustering algorithms on datasets, the optimum feature vector for clustering is determined. For clustering various manifolding techniques are employed. In the suggested method, the graph heat kernel is constructed using industry-standard objects which are taken from the Engineering bench mark Data set.

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Gupta, C. K., B. Shwetha Shetty, and V. Lokesha. "On the graph of nilpotent matrix group of length one." Discrete Mathematics, Algorithms and Applications 08, no. 01 (2016): 1650009. http://dx.doi.org/10.1142/s1793830916500099.

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In this paper we construct a Cayley graph for multiplicative group of upper unitriangular [Formula: see text] matrices over [Formula: see text] mod [Formula: see text]. Also we find some topological indices, diameter, girth, spectra and energy of adjacency, Laplacian, normalized Laplacian and signless Laplacian matrix of the same graph.

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8

Carmona, Ángeles, Margarida Mitjana, and Enric Monsó. "Group inverse matrix of the normalized Laplacian on subdivision networks." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 23. http://dx.doi.org/10.2298/aadm180420023c.

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In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian of the initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both structures and takes advantage on the properties of the group inverse matrix. As a consequence we get formulae for effective resistances and the Kirchhoff Index of the subdivision network expressed in terms of its corresponding in the base network. Finally, we study two examples where the base network are the star and the wheel, respectively.

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9

Kirkland, Steve, and Debdas Paul. "Bipartite subgraphs and the signless Laplacian matrix." Applicable Analysis and Discrete Mathematics 5, no. 1 (2011): 1–13. http://dx.doi.org/10.2298/aadm110205006k.

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For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalized Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs. Our results are applied to some graphs with degree sequences approximately following a power law distribution with exponent value 2:1 (scale-free networks), and to a scale-free network arising from protein-protein interaction.

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10

Braga, R. O., V. M. Rodrigues, and R. O. Silva. "Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic." Trends in Computational and Applied Mathematics 22, no. 4 (2021): 659–74. http://dx.doi.org/10.5540/tcam.2021.022.04.00659.

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We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic. The algorithm can be applied to vertex- and/or edge-weighted or unweighted unicyclic graphs. We apply the algorithm to obtain some general results on the spectrum of a generalized sun graph for certain matrix representations which include the Laplacian, normalized Laplacian and signless Laplacian matrices.

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Conference papers on the topic "Normalized laplacian matrix"

1

Leng, Chengcai, and Haipeng Zhang. "The prediction of eigenvalues of the normalized laplacian matrix for image registration." In 2016 12th International Conference on Natural Computation and 13th Fuzzy Systems and Knowledge Discovery (ICNC-FSKD). IEEE, 2016. http://dx.doi.org/10.1109/fskd.2016.7603419.

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2

Zhang, Yibo, Tian Nan, and Zhaozhi Zhang. "Community Detection in Signed Networks Based on Normalized Laplacian Matrix and Convex Non-negative Matrix Factorization." In 2023 2nd International Conference on Automation, Robotics and Computer Engineering (ICARCE). IEEE, 2023. http://dx.doi.org/10.1109/icarce59252.2024.10492483.

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