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1 <html> | |
2 <head> | |
3 <title>MayaChemTools:Documentation:Graph::GraphMatrix.pm</title> | |
4 <meta http-equiv="content-type" content="text/html;charset=utf-8"> | |
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7 <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10"> | |
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9 <center> | |
10 <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a> | |
11 </center> | |
12 <br/> | |
13 <div class="DocNav"> | |
14 <table width="100%" border=0 cellpadding=0 cellspacing=2> | |
15 <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> | |
16 </table> | |
17 </div> | |
18 <p> | |
19 </p> | |
20 <h2>NAME</h2> | |
21 <p>GraphMatrix</p> | |
22 <p> | |
23 </p> | |
24 <h2>SYNOPSIS</h2> | |
25 <p>use Graph::GraphMatrix;</p> | |
26 <p>use Graph::GraphMatrix qw(:all);</p> | |
27 <p> | |
28 </p> | |
29 <h2>DESCRIPTION</h2> | |
30 <p><strong>GraphMatrix</strong> class provides the following methods:</p> | |
31 <p> <a href="#new">new</a>, <a href="#generateadjacencymatrix">GenerateAdjacencyMatrix</a>, <a href="#generateadmittancematrix">GenerateAdmittanceMatrix</a>, <a href="#generatedegreematrix">GenerateDegreeMatrix</a> | |
32 , <a href="#generatedistancematrix">GenerateDistanceMatrix</a>, <a href="#generateincidencematrix">GenerateIncidenceMatrix</a>, <a href="#generatekirchhoffmatrix">GenerateKirchhoffMatrix</a> | |
33 , <a href="#generatelaplacianmatrix">GenerateLaplacianMatrix</a>, <a href="#generatenormalizedlaplacianmatrix">GenerateNormalizedLaplacianMatrix</a> | |
34 , <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> | |
35 , <a href="#stringifygraphmatrix">StringifyGraphMatrix</a> | |
36 </p><p> | |
37 </p> | |
38 <h2>METHODS</h2> | |
39 <dl> | |
40 <dt><strong><a name="new" class="item"><strong>new</strong></a></strong></dt> | |
41 <dd> | |
42 <div class="OptionsBox"> | |
43 $NewGraphMatrix = new Graph::GraphMatrix($Graph);</div> | |
44 <p>Using specified <em>Graph</em>, <strong>new</strong> method creates a new <strong>GraphMatrix</strong> and returns | |
45 newly created <strong>GraphMatrix</strong>.</p> | |
46 </dd> | |
47 <dt><strong><a name="generateadjacencymatrix" class="item"><strong>GenerateAdjacencyMatrix</strong></a></strong></dt> | |
48 <dd> | |
49 <div class="OptionsBox"> | |
50 $AdjacencyGraphMatrix = $GraphMatrix->GenerateAdjacencyMatrix();</div> | |
51 <p>Generates a new <em>AdjacencyGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
52 <em>AdjacencyGraphMatrix</em>.</p> | |
53 <p>For a simple graph G with n vertices, the adjacency matrix for G is a n x n square matrix and | |
54 its elements Mij are:</p> | |
55 <div class="OptionsBox"> | |
56 . 0 if i == j | |
57 <br/> . 1 if i != j and vertex Vi is adjacent to vertex Vj | |
58 <br/> . 0 if i != j and vertex Vi is not adjacent to vertex Vj</div> | |
59 </dd> | |
60 <dt><strong><a name="generateadmittancematrix" class="item"><strong>GenerateAdmittanceMatrix</strong></a></strong></dt> | |
61 <dd> | |
62 <div class="OptionsBox"> | |
63 $AdmittanceGraphMatrix = $GraphMatrix->GenerateAdmittanceMatrix();</div> | |
64 <p>Generates a new <em>AdmittanceGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
65 <em>AdmittanceGraphMatrix</em>.</p> | |
66 <p><strong>AdmittanceMatrix</strong> is another name for <strong>LaplacianMatrix</strong>.</p> | |
67 </dd> | |
68 <dt><strong><a name="generatedegreematrix" class="item"><strong>GenerateDegreeMatrix</strong></a></strong></dt> | |
69 <dd> | |
70 <div class="OptionsBox"> | |
71 $DegreeGraphMatrix = $GraphMatrix->GenerateDegreeMatrix();</div> | |
72 <p>Generates a new <em>DegreeGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
73 <em>DegreeGraphMatrix</em>.</p> | |
74 <p>For a simple graph G with n vertices, the degree matrix for G is a n x n square matrix and | |
75 its elements Mij are:</p> | |
76 <div class="OptionsBox"> | |
77 . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi | |
78 <br/> . 0 otherwise</div> | |
79 </dd> | |
80 <dt><strong><a name="generatedistancematrix" class="item"><strong>GenerateDistanceMatrix</strong></a></strong></dt> | |
81 <dd> | |
82 <div class="OptionsBox"> | |
83 $DistanceGraphMatrix = $GraphMatrix->GenerateDistanceMatrix();</div> | |
84 <p>Generates a new <em>DistanceGraphMatrix</em> for specified <strong>Graph</strong> using Floyd-Marshall | |
85 algorithm [Ref 67] and returns <em>DistanceGraphMatrix</em>.</p> | |
86 <p>For a simple graph G with n vertices, the distance matrix for G is a n x n square matrix and | |
87 its elements Mij are:</p> | |
88 <div class="OptionsBox"> | |
89 . 0 if i == j | |
90 <br/> . d if i != j and d is the shortest distance between vertex Vi and vertex Vj</div> | |
91 <p>In the final matrix, value of constant <strong>BigNumber</strong> defined in <strong>Constants.pm</strong> module | |
92 corresponds to vertices with no edges.</p> | |
93 </dd> | |
94 <dt><strong><a name="generateincidencematrix" class="item"><strong>GenerateIncidenceMatrix</strong></a></strong></dt> | |
95 <dd> | |
96 <div class="OptionsBox"> | |
97 $IncidenceGraphMatrix = $GraphMatrix->GenerateIncidenceMatrix();</div> | |
98 <p>Generates a new <em>IncidenceGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
99 <em>IncidenceGraphMatrix</em>.</p> | |
100 <p>For a simple graph G with n vertices and e edges, the incidence matrix for G is a n x e matrix | |
101 its elements Mij are:</p> | |
102 <div class="OptionsBox"> | |
103 . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related | |
104 <br/> . 0 otherwise</div> | |
105 </dd> | |
106 <dt><strong><a name="generatekirchhoffmatrix" class="item"><strong>GenerateKirchhoffMatrix</strong></a></strong></dt> | |
107 <dd> | |
108 <div class="OptionsBox"> | |
109 $KirchhoffGraphMatrix = $GraphMatrix->GenerateKirchhoffMatrix();</div> | |
110 <p>Generates a new <em>KirchhoffGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
111 <em>KirchhoffGraphMatrix</em>.</p> | |
112 <p><strong>KirchhoffMatrix</strong> is another name for <strong>LaplacianMatrix</strong>.</p> | |
113 </dd> | |
114 <dt><strong><a name="generatelaplacianmatrix" class="item"><strong>GenerateLaplacianMatrix</strong></a></strong></dt> | |
115 <dd> | |
116 <div class="OptionsBox"> | |
117 $LaplacianGraphMatrix = $GraphMatrix->GenerateLaplacianMatrix();</div> | |
118 <p>Generates a new <em>LaplacianGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
119 <em>LaplacianGraphMatrix</em>.</p> | |
120 <p>For a simple graph G with n vertices, the Laplacian matrix for G is a n x n square matrix and | |
121 its elements Mij are:</p> | |
122 <div class="OptionsBox"> | |
123 . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi | |
124 <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj | |
125 <br/> . 0 otherwise</div> | |
126 <p>The Laplacian matrix is the difference between the degree matrix and adjacency matrix.</p> | |
127 </dd> | |
128 <dt><strong><a name="generatenormalizedlaplacianmatrix" class="item"><strong>GenerateNormalizedLaplacianMatrix</strong></a></strong></dt> | |
129 <dd> | |
130 <div class="OptionsBox"> | |
131 $NormalizedLaplacianGraphMatrix = $GraphMatrix->GenerateNormalizedLaplacianMatrix();</div> | |
132 <p>Generates a new <em>NormalizedLaplacianGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
133 <em>NormalizedLaplacianGraphMatrix</em>.</p> | |
134 <p>For a simple graph G with n vertices, the normalized Laplacian matrix L for G is a n x n square | |
135 matrix and its elements Lij are:</p> | |
136 <div class="OptionsBox"> | |
137 . 1 if i == j and deg(Vi) != 0 | |
138 <br/> . -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj | |
139 <br/> . 0 otherwise</div> | |
140 </dd> | |
141 <dt><strong><a name="generatesiedeladjacencymatrix" class="item"><strong>GenerateSiedelAdjacencyMatrix</strong></a></strong></dt> | |
142 <dd> | |
143 <div class="OptionsBox"> | |
144 $SiedelAdjacencyGraphMatrix = $GraphMatrix->GenerateSiedelAdjacencyMatrix();</div> | |
145 <p>Generates a new <em>SiedelAdjacencyGraphMatrix</em> for specified <strong>Graph</strong> and returns | |
146 <em>SiedelAdjacencyGraphMatrix</em>.</p> | |
147 <p>For a simple graph G with n vertices, the Siedal adjacency matrix for G is a n x n square matrix and | |
148 its elements Mij are:</p> | |
149 <div class="OptionsBox"> | |
150 . 0 if i == j | |
151 <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj | |
152 <br/> . 1 if i != j and vertex Vi is not adjacent to vertex Vj</div> | |
153 </dd> | |
154 <dt><strong><a name="getcolumnids" class="item"><strong>GetColumnIDs</strong></a></strong></dt> | |
155 <dd> | |
156 <div class="OptionsBox"> | |
157 @ColumnIDs = $GraphMatrix->GetColumnIDs();</div> | |
158 <p>Returns an array containing any specified column IDs for <em>GraphMatrix</em>.</p> | |
159 </dd> | |
160 <dt><strong><a name="getmatrix" class="item"><strong>GetMatrix</strong></a></strong></dt> | |
161 <dd> | |
162 <div class="OptionsBox"> | |
163 $Matrix = $GraphMatrix->GetMatrix();</div> | |
164 <p>Returns <em>Matrix</em> object corresponding to <em>GraphMatrix</em> object.</p> | |
165 </dd> | |
166 <dt><strong><a name="getmatrixtype" class="item"><strong>GetMatrixType</strong></a></strong></dt> | |
167 <dd> | |
168 <div class="OptionsBox"> | |
169 $MatrixType = $GraphMatrix->GetMatrixType();</div> | |
170 <p>Returns <strong>MatrixType</strong> of <em>GraphMatrix</em>.</p> | |
171 </dd> | |
172 <dt><strong><a name="getrowids" class="item"><strong>GetRowIDs</strong></a></strong></dt> | |
173 <dd> | |
174 <div class="OptionsBox"> | |
175 @RowIDs = $GraphMatrix->GetRowIDs();</div> | |
176 <p>Returns an array containing any specified rowIDs IDs for <em>GraphMatrix</em>.</p> | |
177 </dd> | |
178 <dt><strong><a name="stringifygraphmatrix" class="item"><strong>StringifyGraphMatrix</strong></a></strong></dt> | |
179 <dd> | |
180 <div class="OptionsBox"> | |
181 $String = $GraphMatrix->StringifyGraphMatrix();</div> | |
182 <p>Returns a string containing information about <em>GraphMatrix</em> object.</p> | |
183 </dd> | |
184 </dl> | |
185 <p> | |
186 </p> | |
187 <h2>AUTHOR</h2> | |
188 <p><a href="mailto:msud@san.rr.com">Manish Sud</a></p> | |
189 <p> | |
190 </p> | |
191 <h2>SEE ALSO</h2> | |
192 <p><a href="./Constants.html">Constants.pm</a>, <a href="./Graph.html">Graph.pm</a>, <a href="./Matrix.html">Matrix.pm</a> | |
193 </p> | |
194 <p> | |
195 </p> | |
196 <h2>COPYRIGHT</h2> | |
197 <p>Copyright (C) 2015 Manish Sud. All rights reserved.</p> | |
198 <p>This file is part of MayaChemTools.</p> | |
199 <p>MayaChemTools is free software; you can redistribute it and/or modify it under | |
200 the terms of the GNU Lesser General Public License as published by the Free | |
201 Software Foundation; either version 3 of the License, or (at your option) | |
202 any later version.</p> | |
203 <p> </p><p> </p><div class="DocNav"> | |
204 <table width="100%" border=0 cellpadding=0 cellspacing=2> | |
205 <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> | |
206 </table> | |
207 </div> | |
208 <br /> | |
209 <center> | |
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213 </html> |