A graph based method for generating the fiedler vector of irregular problems

1999 ◽  
pp. 978-985 ◽  
Author(s):  
Michael Holzrichter ◽  
Suely Oliveira
Keyword(s):  
Fiedler Vector

scholarly journals Fiedler Vector Approximation via Interacting RandomWalks

2020 ◽  
Vol 48 (1) ◽  
pp. 101-102
Author(s):  
Vishwaraj Doshi ◽  
Do Young Eun
Keyword(s):  
Fiedler Vector ◽  
Vector Approximation

Uncovering multiloci-ordering by algebraic property of Laplacian matrix and its Fiedler vector

2015 ◽  
Vol 32 (6) ◽  
pp. 801-807 ◽  
Author(s):  
Mookyung Cheon ◽  
Choongrak Kim ◽  
Iksoo Chang
Keyword(s):  
Source Code ◽  
Algebraic Property ◽  
Laplacian Matrix ◽  
Recombination Fraction ◽  
Supplementary Information ◽  
Supplementary Data ◽  
Data Set ◽  
Variable Threshold ◽  
Fiedler Vector ◽  
Complex Graph

AbstractMotivation: The loci-ordering, based on two-point recombination fractions for a pair of loci, is the most important step in constructing a reliable and fine genetic map.Results: Using the concept from complex graph theory, here we propose a Laplacian ordering approach which uncovers the loci-ordering of multiloci simultaneously. The algebraic property for a Fiedler vector of a Laplacian matrix, constructed from the recombination fraction of the loci-ordering for 26 loci of barley chromosome IV, 846 loci of Arabidopsisthaliana and 1903 loci of Malus domestica, together with the variable threshold uncovers their loci-orders. It offers an alternative yet robust approach for ordering multiloci.Availability and implementation : Source code program with data set is available as supplementary data and also in a software category of the website (http://biophysics.dgist.ac.kr)Contact: [email protected] or [email protected] information: Supplementary data are available at Bioinformatics online.

An Efficient and Accurate Scheme for Computing the Fiedler Vector

2014 ◽  
Vol 36 (11) ◽  
pp. 2266-2273 ◽  
Author(s):  
Jian-Ping WU ◽  
Jun-Qiang SONG ◽  
Wei-Min ZHANG ◽  
Jun ZHAO
Keyword(s):  
Fiedler Vector ◽  
Accurate Scheme

Distributed Fiedler Vector Estimation With Application to Desynchronization of Harmonic Oscillator Networks

2021 ◽  
Vol 5 (2) ◽  
pp. 659-664
Author(s):  
Diego Deplano ◽  
Mauro Franceschelli ◽  
Alessandro Giua ◽  
Luca Scardovi
Keyword(s):  
Harmonic Oscillator ◽  
Oscillator Networks ◽  
Fiedler Vector ◽  
Vector Estimation

Linear Software Models: Bipartite Isomorphism between Laplacian Eigenvectors and Modularity Matrix Eigenvectors

2018 ◽  
Vol 28 (07) ◽  
pp. 897-935 ◽  
Author(s):  
Iaakov Exman ◽  
Rawi Sakhnini
Keyword(s):  
Bipartite Graph ◽  
Algebraic Theory ◽  
Laplacian Matrix ◽  
Connected Components ◽  
Central Importance ◽  
Fiedler Vector ◽  
Software Models ◽  
Suitable Definition ◽  
Software Modularity ◽  
Definition Of

We have recently shown that one can obtain the numbers and sizes of modules of a software system from the eigenvectors of its modularity matrix symmetrized and weighted by an affinity matrix. However such a weighting still demands a suitable definition of an affinity. This paper offers an alternative way to obtain the same results by means of the eigenvectors of a Laplacian matrix, directly obtained from the modularity matrix without the need of weighting. These two formalizations stand in a mutual isomorphism. We call it bipartite isomorphism since it is most straightforwardly shown by deriving the Laplacian from the modularity matrix and vice versa through the intermediate bipartite graph between two separate sets: the structors’ and the functionals’ sets. This isomorphism is also demonstrated through the equation defining the Laplacian in terms of the modularity matrix, or by the direct mapping of the respective matrices’ eigenvectors. Both matrices and the bipartite graph reflect one central idea: modules are connected components with high cohesion. The Laplacian matrix technique, of which the Fiedler vector is of central importance, is illustrated by case studies. An important claim of this paper is that, independently of the modularity matrix- and Laplacian matrix-specific properties, behind these two alternative matrices there is just one unified algebraic theory of software composition — the Linear Software Models — here concerning the application of the matrices’ eigenvectors to software modularity.

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