Resistance distance and the normalized Laplacian spectrum
Haiyan Chen,Fuji Zhang +1 more
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TLDR
Not only is it shown the resistance distance can be naturally expressed in terms of the normalized Laplacian eigenvalues and eigenvectors of G, but also a new index which is closely related to the spectrum of the Normalized LaPLacian is introduced.About:
This article is published in Discrete Applied Mathematics.The article was published on 2007-03-01 and is currently open access. It has received 294 citations till now. The article focuses on the topics: Laplacian matrix & Resistance distance.read more
Citations
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Kirchhoff index of linear hexagonal chains
Yujun Yang,Heping Zhang +1 more
TL;DR: In this paper, the Laplacian spectrum of a linear hexagonal chain Ln was derived in terms of the characteristic polynomial of a symmetric tridiagonal matrix of order 2n + 1.
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A recursion formula for resistance distances and its applications
Yujun Yang,Douglas J. Klein +1 more
TL;DR: A recursion formula for resistance distances is obtained, and some of its applications are illustrated.
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A class of graph-geodetic distances generalizing the shortest-path and the resistance distances
TL;DR: A new class of distances for graph vertices is proposed, which contains parametric families of distances which reduce to the shortest-path, weighted shortest- path, and the resistance distances at the limiting values of the family parameters.
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On the number of spanning trees and normalized Laplacian of linear octagonal‐quadrilateral networks
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On the normalised Laplacian spectrum, degree-Kirchhoff index and spanning trees of graphs
Jing Huang,Shuchao Li +1 more
TL;DR: In this paper, a lower bound for the degree-Kirchhoff index and a formula for the number of spanning trees of a connected regular graph was derived in terms of the normalised Laplacian characteristic polynomial of the graph.
References
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Book
Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
Book
Random walks and electric networks
Peter G. Doyle,J. Laurie Snell +1 more
TL;DR: The goal will be to interpret Polya’s beautiful theorem that a random walker on an infinite street network in d-dimensional space is bound to return to the starting point when d = 2, but has a positive probability of escaping to infinity without returning to the Starting Point when d ≥ 3, and to prove the theorem using techniques from classical electrical theory.
Random Walks on Graphs: A Survey
TL;DR: Estimates on the important parameters of access time, commute time, cover time and mixing time are discussed and recent algorithmic applications of random walks are sketched, in particular to the problem of sampling.
Journal ArticleDOI
Wiener Index of Trees: Theory and Applications
TL;DR: The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph as discussed by the authors, defined as the distance between all vertices in a graph.
Proceedings ArticleDOI
The electrical resistance of a graph captures its commute and cover times
TL;DR: Known bounds on cover times for various classes of graphs, including high-degree graphs, expanders, and multi-dimensional meshes are improved by showing that resistance in this network is intimately connected with the lengths of random walks on the graph.