Results 21 to 30 of about 14,497 (259)
An analog of Matrix Tree Theorem for signless Laplacians [PDF]
Linear Algebra and its Applications, 2019 A spanning tree of a graph is a connected subgraph on all vertices with the minimum number of edges. The number of spanning trees in a graph $G$ is given by Matrix Tree Theorem in terms of principal minors of Laplacian matrix of $G$. We show a similar combinatorial interpretation for principal minors of signless Laplacian $Q$.
Keivan Hassani Monfared, Sudipta Mallik
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Spectral properties for the Laplacian of a generalized Wigner matrix [PDF]
Random Matrices: Theory and Applications, 2021 In this paper, we consider the spectrum of a Laplacian matrix, also known as Markov matrices where the entries of the matrix are independent but have a variance profile. Motivated by recent works on generalized Wigner matrices we assume that the variance profile gives rise to a sequence of graphons.
Chatterjee, A., Hazra, R.S.
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Approximations of the Generalized Inverse of the Graph Laplacian Matrix [PDF]
Internet Mathematics, 2012 We devise methods for finding approximations of the generalized inverse of the graph Laplacian matrix, which arises in many graph-theoretic applications. Finding this matrix in its entirety involves solving a matrix inversion problem, which is resource-demanding in terms of consumed time and memory and hence impractical whenever the graph is relatively
BOZZO, Enrico, FRANCESCHET, Massimo
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More on Spectral Analysis of Signed Networks
Complexity, 2018 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
Guihai Yu, Hui Qu
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Trees with matrix weights: Laplacian matrix and characteristic-like vertices
Linear Algebra and its Applications, 2022 It is known that there is an alternative characterization of characteristic vertices for trees with positive weights on their edges via Perron values and Perron branches. Moreover, the algebraic connectivity of a tree with positive edge weights can be expressed in terms of Perron value.
Swetha Ganesh, Sumit Mohanty
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Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic
Trends in Computational and Applied Mathematics, 2021 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.
R. O. Braga +2 more
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Hermitian Laplacian Matrix of Directed Graphs [PDF]
Jisuanji kexue, 2023 Laplacian matrix plays an important role in the research of undirected graphs.From its spectrum,some structure and properties of a graph can be deduced.Based on this,several efficient algorithms have been designed for relevant tasks in graphs,such as ...
LIU Kaiwen, HUANG Zengfeng
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RECOGNITION OF HUMAN POSE FROM IMAGES BASED ON GRAPH SPECTRA [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2015 Recognition of human pose is an actual problem in computer vision. To increase the reliability of the recognition it is proposed to use structured information in the form of graphs.
A. A. Zakharov +2 more
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The p-spectral radius of the Laplacian matrix
Applicable Analysis and Discrete Mathematics, 2018 The p-spectral radius of a graph G=(V,E) with adjacency matrix A is defined as ?(p)(G) = max||x||p=1 xT Ax. This parameter shows connections with graph invariants, and has been used to generalize some extremal problems. In this work, we define the p-spectral radius of the Laplacian matrix L as ?(p)(G) = max||x||p=1 xT Lx.
Borba, Elizandro Max +3 more
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Spectra of Graphs Resulting from Various Graph Operations and Products: a Survey
Special Matrices, 2018 Let G be a graph on n vertices and A(G), L(G), and |L|(G) be the adjacency matrix, Laplacian matrix and signless Laplacian matrix of G, respectively. The paper is essentially a survey of known results about the spectra of the adjacency, Laplacian and ...
Barik S., Kalita D., Pati S., Sahoo G.
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