Relevant bibliographies by topics / Laplacian matrix

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Laplacian matrix'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 April 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Laplacian matrix.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Laplacian matrix"

1

Zakiyyah, A. Y. "Some result on integrality of several matrix representation of complete r-uniform hypergraph." Journal of Physics: Conference Series 2157, no. 1 (January 1, 2022): 012006. http://dx.doi.org/10.1088/1742-6596/2157/1/012006.

Full text
Abstract:
Abstract The eigenvalues of matrix representation hypergraph have the possibility that all of it can be an integer or otherwise. The Laplacian integral hypergraphs are those hypergraphs whose Laplacian spectrum consists entirely of integers likewise the definition of signless Laplacian integral and Seidel integral. This research focuses on the properties of the entry matrix and formulates the spectrum of the Laplacian matrix, Signless Laplacian matrix, and Seidel Matrix of complete r-uniform hypergraphs. Hence, it can determine the integrality of the representation matrix respectively. The result concludes that complete r-uniform hypergraphs are Laplacian integral, signless Laplacian integral, and Seidel integral.
APA, Harvard, Vancouver, ISO, and other styles
2

Lorenzen, Kate. "Cospectral constructions for several graph matrices using cousin vertices." Special Matrices 10, no. 1 (June 28, 2021): 9–22. http://dx.doi.org/10.1515/spma-2020-0143.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
3

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.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
4

D., Cokilavany. "On Some Bounds of Extended Signless Laplacian Matrix Indices." Journal of Advanced Research in Dynamical and Control Systems 12, SP4 (March 31, 2020): 1816–21. http://dx.doi.org/10.5373/jardcs/v12sp4/20201667.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Wu, Tingzeng, and Tian Zhou. "The Characterizing Properties of (Signless) Laplacian Permanental Polynomials of Almost Complete Graphs." Journal of Mathematics 2021 (September 30, 2021): 1–7. http://dx.doi.org/10.1155/2021/9161508.

Full text
Abstract:
Let G be a graph with n vertices, and let L G and Q G denote the Laplacian matrix and signless Laplacian matrix, respectively. The Laplacian (respectively, signless Laplacian) permanental polynomial of G is defined as the permanent of the characteristic matrix of L G (respectively, Q G ). In this paper, we show that almost complete graphs are determined by their (signless) Laplacian permanental polynomials.
APA, Harvard, Vancouver, ISO, and other styles
6

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 (May 22, 2016): 132. http://dx.doi.org/10.14419/ijamr.v5i2.6106.

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
7

Trinajstic, Nenad, Darko Babic, Sonja Nikolic, Dejan Plavsic, Dragan Amic, and Zlatko Mihalic. "The Laplacian matrix in chemistry." Journal of Chemical Information and Modeling 34, no. 2 (March 1, 1994): 368–76. http://dx.doi.org/10.1021/ci00018a023.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Tuna, S. Emre. "Synchronization under matrix-weighted Laplacian." Automatica 73 (November 2016): 76–81. http://dx.doi.org/10.1016/j.automatica.2016.06.012.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Ameenal Bibi, K., B. Vijayalakshmi, and R. Jothilakshmi. "Bounds of Laplacian Energy of a Hypercube Graph." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 582. http://dx.doi.org/10.14419/ijet.v7i4.10.21287.

Full text
Abstract:
Let Qn denote the n – dimensional hypercube with order 2n and size n2n-1. The Laplacian L is defined by L = D where D is the degree matrix and A is the adjacency matrix with zero diagonal entries. The Laplacian is a symmetric positive semidefinite. Let µ1 ≥ µ2 ≥ ....µn-1 ≥ µn = 0 be the eigen values of the Laplacian matrix. The Laplacian energy is defined as LE(G) = . In this paper, we defined Laplacian energy of a Hypercube graph and also attained the lower bounds.
APA, Harvard, Vancouver, ISO, and other styles
10

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

Full text
Abstract:
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.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Laplacian matrix"

1

Biyikoglu, Türker, and Josef Leydold. "Semiregular Trees with Minimal Laplacian Spectral Radius." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2009. http://epub.wu.ac.at/986/1/document.pdf.

Full text
Abstract:
A semiregular tree is a tree where all non-pendant vertices have the same degree. Among all semiregular trees with fixed order and degree, a graph with minimal (adjacency / Laplacian) spectral radius is a caterpillar. Counter examples show that the result cannot be generalized to the class of trees with a given (non-constant) degree sequence.
Series: Research Report Series / Department of Statistics and Mathematics
APA, Harvard, Vancouver, ISO, and other styles
2

Helmberg, Christoph, Israel Rocha, and Uwe Schwerdtfeger. "A Combinatorial Algorithm for Minimizing the Maximum Laplacian Eigenvalue of Weighted Bipartite Graphs." Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-175057.

Full text
Abstract:
We give a strongly polynomial time combinatorial algorithm to minimise the largest eigenvalue of the weighted Laplacian of a bipartite graph. This is accomplished by solving the dual graph embedding problem which arises from a semidefinite programming formulation. In particular, the problem for trees can be solved in time cubic in the number of vertices.
APA, Harvard, Vancouver, ISO, and other styles
3

Meyer, Marie. "Polytopes Associated to Graph Laplacians." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/54.

Full text
Abstract:
Graphs provide interesting ways to generate families of lattice polytopes. In particular, one can use matrices encoding the information of a finite graph to define vertices of a polytope. This dissertation initiates the study of the Laplacian simplex, PG, obtained from a finite graph G by taking the convex hull of the columns of the Laplacian matrix for G. The Laplacian simplex is extended through the use of a parallel construction with a finite digraph D to obtain the Laplacian polytope, PD. Basic properties of both families of simplices, PG and PD, are established using techniques from Ehrhart theory. Motivated by a well-known conjecture in the field, our investigation focuses on reflexivity, the integer decomposition property, and unimodality of Ehrhart h*-vectors of these polytopes. A systematic investigation of PG for trees, cycles, and complete graphs is provided, which is enhanced by an investigation of PD for cyclic digraphs. We form intriguing connections with other families of simplices and produce G and D such that the h*-vectors of PG and PD exhibit extremal behavior.
APA, Harvard, Vancouver, ISO, and other styles
4

Braga, Rodrigo Orsini. "Localização de autovalores de árvores e de grafos unicíclicos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/132255.

Full text
Abstract:
Neste trabalho, apresentamos um algoritmo que determina o número de autovalores de uma matriz simétrica qualquer que representa uma árvore, num dado intervalo real. Várias aplicações são obtidas em relação à distribuição dos autovalores da matriz laplaciana perturbada, uma matriz de representação de grafos que inclui, como casos particulares, a matriz de adjacências, a matriz laplaciana combinatória, a matriz laplaciana sem sinal e a matriz laplaciana normalizada, amplamente estudadas em Teoria Espectral de Grafos. Além disso, desenvolvemos também um algoritmo de localização de autovalores da matriz de adjacências de um grafo unicíclico. Este procedimento permite obter propriedades espectrais de grafos unicíclicos denominados centopeias unicíclicas.
In this work, we present an algorithm that computes the number of eigenvalues of any symmetric matrix that represents a tree, in a given real interval. Several applications are obtained about the distribution of the eigenvalues of the perturbed Laplacian matrix, which is a matrix representation of graphs that includes, as special cases, the adjacency matrix, the combinatorial Laplacian matrix, the signless Laplacian matrix and the normalized Laplacian matrix, widely studied in Spectral Graph Theory. In addition, we also develop an algorithm that locates the eigenvalues of the adjacency matrix of a unicyclic graph. This procedure allows us to obtain spectral properties of unicyclic caterpillars.
APA, Harvard, Vancouver, ISO, and other styles
5

Biyikoglu, Türker, and Josef Leydold. "Algebraic Connectivity and Degree Sequences of Trees." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2008. http://epub.wu.ac.at/782/1/document.pdf.

Full text
Abstract:
We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on non-pendant vertices starting at the characteristic set of the Fiedler vector. (author´s abstract)
Series: Research Report Series / Department of Statistics and Mathematics
APA, Harvard, Vancouver, ISO, and other styles
6

Brooks, Josh Daniel. "Nested (2,r)-regular graphs and their network properties." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etd/1471.

Full text
Abstract:
A graph G is a (t, r)-regular graph if every collection of t independent vertices is collectively adjacent to exactly r vertices. If a graph G is (2, r)-regular where p, s, and m are positive integers, and m ≥ 2, then when n is sufficiently large, then G is isomorphic to G = Ks+mKp, where 2(p-1)+s = r. A nested (2,r)-regular graph is constructed by replacing selected cliques with a (2,r)-regular graph and joining the vertices of the peripheral cliques. For example, in a nested 's' graph when n = s + mp, we obtain n = s1+m1p1+mp. The nested 's' graph is now of the form Gs = Ks1+m1Kp1+mKp. We examine the network properties such as the average path length, clustering coefficient, and the spectrum of these nested graphs.
APA, Harvard, Vancouver, ISO, and other styles
7

Simpson, Daniel Peter. "Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion." Queensland University of Technology, 2008. http://eprints.qut.edu.au/29751/.

Full text
Abstract:
Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A..=2b, where A 2 Rnn is a large, sparse symmetric positive definite matrix and b 2 Rn is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LLT is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L..T z, with x = A..1=2z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form n = A..=2b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t..=2 and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A..=2b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.
APA, Harvard, Vancouver, ISO, and other styles
8

Amaro, Bruno Dias 1984. "A soma dos maiores autovalores da matriz laplaciana sem sinal em famílias de grafos." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306808.

Full text
Abstract:
Orientadores: Carlile Campos Lavor, Leonardo Silva de Lima
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-26T08:31:47Z (GMT). No. of bitstreams: 1 Amaro_BrunoDias_D.pdf: 1369520 bytes, checksum: a36663d5fd23193d66bb22c83cb932aa (MD5) Previous issue date: 2014
Resumo: A Teoria Espectral de Grafos é um ramo da Matemática Discreta que se preocupa com a relação entre as propriedades algébricas do espectro de certas matrizes associadas a grafos, como a matriz de adjacência, laplaciana ou laplaciana sem sinal e a topologia dos mesmos. Os autovalores e autovetores das matrizes associadas a um grafo são os invariantes que formam o autoespaço de grafos. Em Teoria Espectral de Grafos a conjectura proposta por Brouwer e Haemers, que associa a soma dos k maiores autovalores da matriz Laplaciana de um grafo G com seu número de arestas mais um fator combinatório (que depende do valor k adotado) é uma das questões interessantes e que está em aberto na literatura. Essa mostra diversos trabalhos que tentam provar tal conjectura. Em 2013, Ashraf et al. estenderam essa conjectura para a matriz laplaciana sem sinal e provaram que ela é válida para a soma dos 2 maiores autovalores e que também é válida para todo k, caso o grafo seja regular. Nosso trabalho aborda a versão dessa conjectura para a matriz laplaciana sem sinal. Conseguimos obter uma família de grafos que satisfaz a conjectura para a soma dos 3 maiores autovalores da matriz laplaciana sem sinal e a família de grafos split completo mais uma aresta satisfaz a conjectura para todos os autovalores. Ainda, baseado na desigualdade de Schur, conseguimos mostrar que a soma dos k menores autovalores das matrizes laplaciana e laplaciana sem sinal são limitadas superiormente pela soma dos k menores graus de G
Abstract: The Spectral Graph Theory is a branch of Discrete Mathematics that is concerned with relations between the algebraic properties of spectrum of some matrices associated to graphs, as the Adjacency, Laplacian and signless Laplacian matrices and their respective topologies. The eigenvalues and eigenvectors of matrices associated to graphs are the invariants which constitute the eigenspace of graphs. On Spectral Graph Theory the conjecture proposed by Brouwer and Haemers, associating the sum of k largest eigenvalues of Laplacian matrix of a graph G with its edges numbers plus a combinatorial factor (which depends on the choosed k) is an open interesting question in the Literature. There are several works that attempt to prove this conjecture. In 2013, Ashraf et al. stretch the conjecture out to signless Laplacian matrix and proved that it is true for the sum of the 2 largest eigenvalues of signless Laplacian matrix and it is also true for all k if G is a regular graph. Our work approaches on the version of the conjecture concerning to signless Laplacian matrix. We could obtain a family of graphs which satisfies the conjecture for the sum of the 3 largest eigenvalues of signless Laplacian matrix and we prove that the family of complete split graphs plus one edge satisfies the Conjecture for all eigenvalues. Moreover, based on Schur's inequality, we could show that the sum of the k smallest eigenvalues of Laplacian and signless Laplacian matrices are bounded by the sum of the k smallest degrees of G
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
APA, Harvard, Vancouver, ISO, and other styles
9

Biyikoglu, Türker. "A Discrete Nodal Domain Theorem for Trees." Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 2002. http://epub.wu.ac.at/1270/1/document.pdf.

Full text
Abstract:
Let G be a connected graph with n vertices and let x=(x1, ..., xn) be a real vector. A positive (negative) sign graph of the vector x is a maximal connected subgraph of G on vertices xi>0 (xi<0). For an eigenvalue of a generalized Laplacian of a tree: We characterize the maximal number of sign graphs of an eigenvector. We give an O(n2) time algorithm to find an eigenvector with maximum number of sign graphs and we show that finding an eigenvector with minimum number of sign graphs is an NP-complete problem. (author's abstract)
Series: Preprint Series / Department of Applied Statistics and Data Processing
APA, Harvard, Vancouver, ISO, and other styles
10

Masum, Mohammad. "Vertex Weighted Spectral Clustering." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3266.

Full text
Abstract:
Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to zero compared to the largest Fiedler coefficient of the graph. We propose a vertex-weighted spectral clustering algorithm which incorporates a vector of weights for each vertex of a given graph to form a vertex-weighted graph. The proposed algorithm predicts association of equidistant or nearly equidistant data points from both clusters while the unweighted clustering does not provide association. Finally, we implemented both the unweighted and the vertex-weighted spectral clustering algorithms on several data sets to show that the proposed algorithm works in general.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Laplacian matrix"

1

Applications of combinatorial matrix theory to Laplacian matrices of graphs. Boca Raton: CRC Press, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Molitierno, Jason J. Applications of combinatorial matrix theory to Laplacian matrices of graphs. Boca Raton: CRC Press, 2012.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Ferrari, Patrik L., and Herbert Spohn. Random matrices and Laplacian growth. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.39.

Full text
Abstract:
This article reviews the theory of random matrices with eigenvalues distributed in the complex plane and more general ‘beta ensembles’ (logarithmic gases in 2D). It first considers two ensembles of random matrices with complex eigenvalues: ensemble C of general complex matrices and ensemble N of normal matrices. In particular, it describes the Dyson gas picture for ensembles of matrices with general complex eigenvalues distributed on the plane. It then presents some general exact relations for correlation functions valid for any values of N and β before analysing the distribution and correlations of the eigenvalues in the large N limit. Using the technique of boundary value problems in two dimensions and elements of the potential theory, the article demonstrates that the finite-time blow-up (a cusp–like singularity) of the Laplacian growth with zero surface tension is a critical point of the normal and complex matrix models.
APA, Harvard, Vancouver, ISO, and other styles
4

Newman, Mark. Mathematics of networks. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805090.003.0006.

Full text
Abstract:
An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.
APA, Harvard, Vancouver, ISO, and other styles
5

Vernizzi, Graziano, and Henri Orland. Complex networks. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.43.

Full text
Abstract:
This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Laplacian matrix"

1

Bapat, Ravindra B. "Laplacian Matrix." In Universitext, 49–59. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6569-9_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Gustafsson, Björn, Razvan Teodorescu, and Alexander Vasil’ev. "Laplacian Growth and Random Matrix Theory." In Classical and Stochastic Laplacian Growth, 187–210. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08287-5_6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Babarinsa, Olayiwola, and Hailiza Kamarulhaili. "On Determinant of Laplacian Matrix and Signless Laplacian Matrix of a Simple Graph." In Theoretical Computer Science and Discrete Mathematics, 212–17. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64419-6_28.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Wiskott, Laurenz, and Fabian Schönfeld. "Laplacian Matrix for Dimensionality Reduction and Clustering." In Lecture Notes in Business Information Processing, 93–119. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61627-4_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Bapat, R. B., and Sivaramakrishnan Sivasubramanian. "The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs." In Combinatorial Matrix Theory and Generalized Inverses of Matrices, 33–40. India: Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1053-5_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Chen, Pan, Yangcheng He, Hongtao Lu, and Li Wu. "Constrained Non-negative Matrix Factorization with Graph Laplacian." In Neural Information Processing, 635–44. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-26555-1_72.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Chen, Xingguang, and Zhentao Zhu. "General Quasi-Laplacian Matrix of Weighted Mixed Pseudograph." In Advances in Intelligent Systems and Computing, 316–23. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02116-0_37.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Kalita, Debajit. "Determinant of the Laplacian Matrix of a Weighted Directed Graph." In Combinatorial Matrix Theory and Generalized Inverses of Matrices, 57–62. India: Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1053-5_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Kirkland, Stephen. "The Group Inverse of the Laplacian Matrix of a Graph." In Advanced Courses in Mathematics - CRM Barcelona, 131–71. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70953-6_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Fiedler, Miroslav. "A Geometric Approach to the Laplacian Matrix of a Graph." In Combinatorial and Graph-Theoretical Problems in Linear Algebra, 73–98. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4613-8354-3_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Laplacian matrix"

1

Wang, Xiangrong, and Piet Van Mieghem. "Orthogonal Eigenvector Matrix of the Laplacian." In 2015 11th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS). IEEE, 2015. http://dx.doi.org/10.1109/sitis.2015.35.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Le Bars, Batiste, Pierre Humbert, Laurent Oudre, and Argyris Kalogeratos. "Learning Laplacian Matrix from Bandlimited Graph Signals." In ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2019. http://dx.doi.org/10.1109/icassp.2019.8682769.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Li, Shuang, and Weiguo Xia. "Sampled-Data Synchronization under Matrix-Weighted Laplacian." In 2019 Chinese Control Conference (CCC). IEEE, 2019. http://dx.doi.org/10.23919/chicc.2019.8865774.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Dong, Xiaowen, Dorina Thanou, Pascal Frossard, and Pierre Vandergheynst. "Laplacian matrix learning for smooth graph signal representation." In ICASSP 2015 - 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2015. http://dx.doi.org/10.1109/icassp.2015.7178669.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Liao, Tianxing, Wen-Qin Wang, Bang Huang, and Jian Xu. "Learning Laplacian Matrix for Smooth Signals on Graph*." In 2019 IEEE International Conference on Signal, Information and Data Processing (ICSIDP). IEEE, 2019. http://dx.doi.org/10.1109/icsidp47821.2019.9173468.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Hou, Junhui, Lap-Pui Chau, Ying He, and Huanqiang Zeng. "Robust laplacian matrix learning for smooth graph signals." In 2016 IEEE International Conference on Image Processing (ICIP). IEEE, 2016. http://dx.doi.org/10.1109/icip.2016.7532684.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Pavez, Eduardo, and Antonio Ortega. "Generalized Laplacian precision matrix estimation for graph signal processing." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472899.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Lam, Edmund Y. "Non-negative matrix factorization for images with Laplacian noise." In APCCAS 2008 - 2008 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS). IEEE, 2008. http://dx.doi.org/10.1109/apccas.2008.4746143.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Hermann, Jonathan, and Ulrich Konigorski. "Eigenvalue Assignment for the Laplacian Matrix of Directed Graphs." In 2019 American Control Conference (ACC). IEEE, 2019. http://dx.doi.org/10.23919/acc.2019.8814446.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Exman, Iaakov, and Rawi Sakhnini. "Linear Software Models: Modularity Analysis by the Laplacian Matrix." In 11th International Conference on Software Paradigm Trends. SCITEPRESS - Science and Technology Publications, 2016. http://dx.doi.org/10.5220/0005985601000108.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Laplacian matrix' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography