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<html> <head> <title>MayaChemTools:Documentation:Graph::GraphMatrix.pm</title> <meta http-equiv="content-type" content="text/html;charset=utf-8"> <link rel="stylesheet" type="text/css" href="../../css/MayaChemTools.css"> </head> <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10"> <br/> <center> <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a> </center> <br/> <div class="DocNav"> <table width="100%" border=0 cellpadding=0 cellspacing=2> <tr align="left" valign="top"><td width="33%" align="left"><a href="./CyclesDetection.html" title="CyclesDetection.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./Path.html" title="Path.html">Next</a></td><td width="34%" align="middle"><strong>Graph::GraphMatrix.pm</strong></td><td width="33%" align="right"><a href="././code/GraphMatrix.html" title="View source code">Code</a> | <a href="./../pdf/GraphMatrix.pdf" title="PDF US Letter Size">PDF</a> | <a href="./../pdfgreen/GraphMatrix.pdf" title="PDF US Letter Size with narrow margins: www.changethemargins.com">PDFGreen</a> | <a href="./../pdfa4/GraphMatrix.pdf" title="PDF A4 Size">PDFA4</a> | <a href="./../pdfa4green/GraphMatrix.pdf" title="PDF A4 Size with narrow margins: www.changethemargins.com">PDFA4Green</a></td></tr> </table> </div> <p> </p> <h2>NAME</h2> <p>GraphMatrix</p> <p> </p> <h2>SYNOPSIS</h2> <p>use Graph::GraphMatrix;</p> <p>use Graph::GraphMatrix qw(:all);</p> <p> </p> <h2>DESCRIPTION</h2> <p><strong>GraphMatrix</strong> class provides the following methods:</p> <p> <a href="#new">new</a>, <a href="#generateadjacencymatrix">GenerateAdjacencyMatrix</a>, <a href="#generateadmittancematrix">GenerateAdmittanceMatrix</a>, <a href="#generatedegreematrix">GenerateDegreeMatrix</a> , <a href="#generatedistancematrix">GenerateDistanceMatrix</a>, <a href="#generateincidencematrix">GenerateIncidenceMatrix</a>, <a href="#generatekirchhoffmatrix">GenerateKirchhoffMatrix</a> , <a href="#generatelaplacianmatrix">GenerateLaplacianMatrix</a>, <a href="#generatenormalizedlaplacianmatrix">GenerateNormalizedLaplacianMatrix</a> , <a href="#generatesiedeladjacencymatrix">GenerateSiedelAdjacencyMatrix</a>, <a href="#getcolumnids">GetColumnIDs</a>, <a href="#getmatrix">GetMatrix</a>, <a href="#getmatrixtype">GetMatrixType</a>, <a href="#getrowids">GetRowIDs</a> , <a href="#stringifygraphmatrix">StringifyGraphMatrix</a> </p><p> </p> <h2>METHODS</h2> <dl> <dt><strong><a name="new" class="item"><strong>new</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NewGraphMatrix = new Graph::GraphMatrix($Graph);</div> <p>Using specified <em>Graph</em>, <strong>new</strong> method creates a new <strong>GraphMatrix</strong> and returns newly created <strong>GraphMatrix</strong>.</p> </dd> <dt><strong><a name="generateadjacencymatrix" class="item"><strong>GenerateAdjacencyMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $AdjacencyGraphMatrix = $GraphMatrix->GenerateAdjacencyMatrix();</div> <p>Generates a new <em>AdjacencyGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>AdjacencyGraphMatrix</em>.</p> <p>For a simple graph G with n vertices, the adjacency matrix for G is a n x n square matrix and its elements Mij are:</p> <div class="OptionsBox"> . 0 if i == j <br/> . 1 if i != j and vertex Vi is adjacent to vertex Vj <br/> . 0 if i != j and vertex Vi is not adjacent to vertex Vj</div> </dd> <dt><strong><a name="generateadmittancematrix" class="item"><strong>GenerateAdmittanceMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $AdmittanceGraphMatrix = $GraphMatrix->GenerateAdmittanceMatrix();</div> <p>Generates a new <em>AdmittanceGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>AdmittanceGraphMatrix</em>.</p> <p><strong>AdmittanceMatrix</strong> is another name for <strong>LaplacianMatrix</strong>.</p> </dd> <dt><strong><a name="generatedegreematrix" class="item"><strong>GenerateDegreeMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $DegreeGraphMatrix = $GraphMatrix->GenerateDegreeMatrix();</div> <p>Generates a new <em>DegreeGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>DegreeGraphMatrix</em>.</p> <p>For a simple graph G with n vertices, the degree matrix for G is a n x n square matrix and its elements Mij are:</p> <div class="OptionsBox"> . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi <br/> . 0 otherwise</div> </dd> <dt><strong><a name="generatedistancematrix" class="item"><strong>GenerateDistanceMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $DistanceGraphMatrix = $GraphMatrix->GenerateDistanceMatrix();</div> <p>Generates a new <em>DistanceGraphMatrix</em> for specified <strong>Graph</strong> using Floyd-Marshall algorithm [Ref 67] and returns <em>DistanceGraphMatrix</em>.</p> <p>For a simple graph G with n vertices, the distance matrix for G is a n x n square matrix and its elements Mij are:</p> <div class="OptionsBox"> . 0 if i == j <br/> . d if i != j and d is the shortest distance between vertex Vi and vertex Vj</div> <p>In the final matrix, value of constant <strong>BigNumber</strong> defined in <strong>Constants.pm</strong> module corresponds to vertices with no edges.</p> </dd> <dt><strong><a name="generateincidencematrix" class="item"><strong>GenerateIncidenceMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $IncidenceGraphMatrix = $GraphMatrix->GenerateIncidenceMatrix();</div> <p>Generates a new <em>IncidenceGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>IncidenceGraphMatrix</em>.</p> <p>For a simple graph G with n vertices and e edges, the incidence matrix for G is a n x e matrix its elements Mij are:</p> <div class="OptionsBox"> . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related <br/> . 0 otherwise</div> </dd> <dt><strong><a name="generatekirchhoffmatrix" class="item"><strong>GenerateKirchhoffMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $KirchhoffGraphMatrix = $GraphMatrix->GenerateKirchhoffMatrix();</div> <p>Generates a new <em>KirchhoffGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>KirchhoffGraphMatrix</em>.</p> <p><strong>KirchhoffMatrix</strong> is another name for <strong>LaplacianMatrix</strong>.</p> </dd> <dt><strong><a name="generatelaplacianmatrix" class="item"><strong>GenerateLaplacianMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $LaplacianGraphMatrix = $GraphMatrix->GenerateLaplacianMatrix();</div> <p>Generates a new <em>LaplacianGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>LaplacianGraphMatrix</em>.</p> <p>For a simple graph G with n vertices, the Laplacian matrix for G is a n x n square matrix and its elements Mij are:</p> <div class="OptionsBox"> . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj <br/> . 0 otherwise</div> <p>The Laplacian matrix is the difference between the degree matrix and adjacency matrix.</p> </dd> <dt><strong><a name="generatenormalizedlaplacianmatrix" class="item"><strong>GenerateNormalizedLaplacianMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NormalizedLaplacianGraphMatrix = $GraphMatrix->GenerateNormalizedLaplacianMatrix();</div> <p>Generates a new <em>NormalizedLaplacianGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>NormalizedLaplacianGraphMatrix</em>.</p> <p>For a simple graph G with n vertices, the normalized Laplacian matrix L for G is a n x n square matrix and its elements Lij are:</p> <div class="OptionsBox"> . 1 if i == j and deg(Vi) != 0 <br/> . -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj <br/> . 0 otherwise</div> </dd> <dt><strong><a name="generatesiedeladjacencymatrix" class="item"><strong>GenerateSiedelAdjacencyMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $SiedelAdjacencyGraphMatrix = $GraphMatrix->GenerateSiedelAdjacencyMatrix();</div> <p>Generates a new <em>SiedelAdjacencyGraphMatrix</em> for specified <strong>Graph</strong> and returns <em>SiedelAdjacencyGraphMatrix</em>.</p> <p>For a simple graph G with n vertices, the Siedal adjacency matrix for G is a n x n square matrix and its elements Mij are:</p> <div class="OptionsBox"> . 0 if i == j <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj <br/> . 1 if i != j and vertex Vi is not adjacent to vertex Vj</div> </dd> <dt><strong><a name="getcolumnids" class="item"><strong>GetColumnIDs</strong></a></strong></dt> <dd> <div class="OptionsBox"> @ColumnIDs = $GraphMatrix->GetColumnIDs();</div> <p>Returns an array containing any specified column IDs for <em>GraphMatrix</em>.</p> </dd> <dt><strong><a name="getmatrix" class="item"><strong>GetMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Matrix = $GraphMatrix->GetMatrix();</div> <p>Returns <em>Matrix</em> object corresponding to <em>GraphMatrix</em> object.</p> </dd> <dt><strong><a name="getmatrixtype" class="item"><strong>GetMatrixType</strong></a></strong></dt> <dd> <div class="OptionsBox"> $MatrixType = $GraphMatrix->GetMatrixType();</div> <p>Returns <strong>MatrixType</strong> of <em>GraphMatrix</em>.</p> </dd> <dt><strong><a name="getrowids" class="item"><strong>GetRowIDs</strong></a></strong></dt> <dd> <div class="OptionsBox"> @RowIDs = $GraphMatrix->GetRowIDs();</div> <p>Returns an array containing any specified rowIDs IDs for <em>GraphMatrix</em>.</p> </dd> <dt><strong><a name="stringifygraphmatrix" class="item"><strong>StringifyGraphMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $String = $GraphMatrix->StringifyGraphMatrix();</div> <p>Returns a string containing information about <em>GraphMatrix</em> object.</p> </dd> </dl> <p> </p> <h2>AUTHOR</h2> <p><a href="mailto:msud@san.rr.com">Manish Sud</a></p> <p> </p> <h2>SEE ALSO</h2> <p><a href="./Constants.html">Constants.pm</a>, <a href="./Graph.html">Graph.pm</a>, <a href="./Matrix.html">Matrix.pm</a> </p> <p> </p> <h2>COPYRIGHT</h2> <p>Copyright (C) 2015 Manish Sud. All rights reserved.</p> <p>This file is part of MayaChemTools.</p> <p>MayaChemTools is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.</p> <p> </p><p> </p><div class="DocNav"> <table width="100%" border=0 cellpadding=0 cellspacing=2> <tr align="left" valign="top"><td width="33%" align="left"><a href="./CyclesDetection.html" title="CyclesDetection.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./Path.html" title="Path.html">Next</a></td><td width="34%" align="middle"><strong>March 29, 2015</strong></td><td width="33%" align="right"><strong>Graph::GraphMatrix.pm</strong></td></tr> </table> </div> <br /> <center> <img src="../../images/h2o2.png"> </center> </body> </html>