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3 <title>MayaChemTools:Documentation:Graph::GraphMatrix.pm</title>
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13 <div class="DocNav">
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14 <table width="100%" border=0 cellpadding=0 cellspacing=2>
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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>
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16 </table>
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17 </div>
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18 <p>
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19 </p>
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20 <h2>NAME</h2>
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21 <p>GraphMatrix</p>
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22 <p>
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23 </p>
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24 <h2>SYNOPSIS</h2>
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25 <p>use Graph::GraphMatrix;</p>
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26 <p>use Graph::GraphMatrix qw(:all);</p>
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27 <p>
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28 </p>
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29 <h2>DESCRIPTION</h2>
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30 <p><strong>GraphMatrix</strong> class provides the following methods:</p>
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31 <p> <a href="#new">new</a>, <a href="#generateadjacencymatrix">GenerateAdjacencyMatrix</a>, <a href="#generateadmittancematrix">GenerateAdmittanceMatrix</a>, <a href="#generatedegreematrix">GenerateDegreeMatrix</a>
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32 , <a href="#generatedistancematrix">GenerateDistanceMatrix</a>, <a href="#generateincidencematrix">GenerateIncidenceMatrix</a>, <a href="#generatekirchhoffmatrix">GenerateKirchhoffMatrix</a>
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33 , <a href="#generatelaplacianmatrix">GenerateLaplacianMatrix</a>, <a href="#generatenormalizedlaplacianmatrix">GenerateNormalizedLaplacianMatrix</a>
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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>
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35 , <a href="#stringifygraphmatrix">StringifyGraphMatrix</a>
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36 </p><p>
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37 </p>
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38 <h2>METHODS</h2>
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39 <dl>
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40 <dt><strong><a name="new" class="item"><strong>new</strong></a></strong></dt>
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41 <dd>
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42 <div class="OptionsBox">
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43 $NewGraphMatrix = new Graph::GraphMatrix($Graph);</div>
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44 <p>Using specified <em>Graph</em>, <strong>new</strong> method creates a new <strong>GraphMatrix</strong> and returns
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45 newly created <strong>GraphMatrix</strong>.</p>
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46 </dd>
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47 <dt><strong><a name="generateadjacencymatrix" class="item"><strong>GenerateAdjacencyMatrix</strong></a></strong></dt>
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48 <dd>
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49 <div class="OptionsBox">
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50 $AdjacencyGraphMatrix = $GraphMatrix->GenerateAdjacencyMatrix();</div>
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51 <p>Generates a new <em>AdjacencyGraphMatrix</em> for specified <strong>Graph</strong> and returns
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52 <em>AdjacencyGraphMatrix</em>.</p>
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53 <p>For a simple graph G with n vertices, the adjacency matrix for G is a n x n square matrix and
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54 its elements Mij are:</p>
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55 <div class="OptionsBox">
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56 . 0 if i == j
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57 <br/> . 1 if i != j and vertex Vi is adjacent to vertex Vj
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58 <br/> . 0 if i != j and vertex Vi is not adjacent to vertex Vj</div>
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59 </dd>
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60 <dt><strong><a name="generateadmittancematrix" class="item"><strong>GenerateAdmittanceMatrix</strong></a></strong></dt>
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61 <dd>
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62 <div class="OptionsBox">
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63 $AdmittanceGraphMatrix = $GraphMatrix->GenerateAdmittanceMatrix();</div>
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64 <p>Generates a new <em>AdmittanceGraphMatrix</em> for specified <strong>Graph</strong> and returns
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65 <em>AdmittanceGraphMatrix</em>.</p>
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66 <p><strong>AdmittanceMatrix</strong> is another name for <strong>LaplacianMatrix</strong>.</p>
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67 </dd>
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68 <dt><strong><a name="generatedegreematrix" class="item"><strong>GenerateDegreeMatrix</strong></a></strong></dt>
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69 <dd>
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70 <div class="OptionsBox">
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71 $DegreeGraphMatrix = $GraphMatrix->GenerateDegreeMatrix();</div>
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72 <p>Generates a new <em>DegreeGraphMatrix</em> for specified <strong>Graph</strong> and returns
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73 <em>DegreeGraphMatrix</em>.</p>
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74 <p>For a simple graph G with n vertices, the degree matrix for G is a n x n square matrix and
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75 its elements Mij are:</p>
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76 <div class="OptionsBox">
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77 . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
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78 <br/> . 0 otherwise</div>
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79 </dd>
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80 <dt><strong><a name="generatedistancematrix" class="item"><strong>GenerateDistanceMatrix</strong></a></strong></dt>
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81 <dd>
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82 <div class="OptionsBox">
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83 $DistanceGraphMatrix = $GraphMatrix->GenerateDistanceMatrix();</div>
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84 <p>Generates a new <em>DistanceGraphMatrix</em> for specified <strong>Graph</strong> using Floyd-Marshall
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85 algorithm [Ref 67] and returns <em>DistanceGraphMatrix</em>.</p>
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86 <p>For a simple graph G with n vertices, the distance matrix for G is a n x n square matrix and
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87 its elements Mij are:</p>
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88 <div class="OptionsBox">
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89 . 0 if i == j
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90 <br/> . d if i != j and d is the shortest distance between vertex Vi and vertex Vj</div>
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91 <p>In the final matrix, value of constant <strong>BigNumber</strong> defined in <strong>Constants.pm</strong> module
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92 corresponds to vertices with no edges.</p>
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93 </dd>
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94 <dt><strong><a name="generateincidencematrix" class="item"><strong>GenerateIncidenceMatrix</strong></a></strong></dt>
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95 <dd>
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96 <div class="OptionsBox">
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97 $IncidenceGraphMatrix = $GraphMatrix->GenerateIncidenceMatrix();</div>
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98 <p>Generates a new <em>IncidenceGraphMatrix</em> for specified <strong>Graph</strong> and returns
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99 <em>IncidenceGraphMatrix</em>.</p>
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100 <p>For a simple graph G with n vertices and e edges, the incidence matrix for G is a n x e matrix
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101 its elements Mij are:</p>
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102 <div class="OptionsBox">
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103 . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related
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104 <br/> . 0 otherwise</div>
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105 </dd>
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106 <dt><strong><a name="generatekirchhoffmatrix" class="item"><strong>GenerateKirchhoffMatrix</strong></a></strong></dt>
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107 <dd>
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108 <div class="OptionsBox">
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109 $KirchhoffGraphMatrix = $GraphMatrix->GenerateKirchhoffMatrix();</div>
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110 <p>Generates a new <em>KirchhoffGraphMatrix</em> for specified <strong>Graph</strong> and returns
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111 <em>KirchhoffGraphMatrix</em>.</p>
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112 <p><strong>KirchhoffMatrix</strong> is another name for <strong>LaplacianMatrix</strong>.</p>
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113 </dd>
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114 <dt><strong><a name="generatelaplacianmatrix" class="item"><strong>GenerateLaplacianMatrix</strong></a></strong></dt>
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115 <dd>
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116 <div class="OptionsBox">
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117 $LaplacianGraphMatrix = $GraphMatrix->GenerateLaplacianMatrix();</div>
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118 <p>Generates a new <em>LaplacianGraphMatrix</em> for specified <strong>Graph</strong> and returns
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119 <em>LaplacianGraphMatrix</em>.</p>
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120 <p>For a simple graph G with n vertices, the Laplacian matrix for G is a n x n square matrix and
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121 its elements Mij are:</p>
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122 <div class="OptionsBox">
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123 . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
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124 <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj
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125 <br/> . 0 otherwise</div>
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126 <p>The Laplacian matrix is the difference between the degree matrix and adjacency matrix.</p>
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127 </dd>
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128 <dt><strong><a name="generatenormalizedlaplacianmatrix" class="item"><strong>GenerateNormalizedLaplacianMatrix</strong></a></strong></dt>
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129 <dd>
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130 <div class="OptionsBox">
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131 $NormalizedLaplacianGraphMatrix = $GraphMatrix->GenerateNormalizedLaplacianMatrix();</div>
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132 <p>Generates a new <em>NormalizedLaplacianGraphMatrix</em> for specified <strong>Graph</strong> and returns
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133 <em>NormalizedLaplacianGraphMatrix</em>.</p>
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134 <p>For a simple graph G with n vertices, the normalized Laplacian matrix L for G is a n x n square
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135 matrix and its elements Lij are:</p>
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136 <div class="OptionsBox">
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137 . 1 if i == j and deg(Vi) != 0
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138 <br/> . -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj
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139 <br/> . 0 otherwise</div>
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140 </dd>
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141 <dt><strong><a name="generatesiedeladjacencymatrix" class="item"><strong>GenerateSiedelAdjacencyMatrix</strong></a></strong></dt>
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142 <dd>
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143 <div class="OptionsBox">
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144 $SiedelAdjacencyGraphMatrix = $GraphMatrix->GenerateSiedelAdjacencyMatrix();</div>
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145 <p>Generates a new <em>SiedelAdjacencyGraphMatrix</em> for specified <strong>Graph</strong> and returns
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146 <em>SiedelAdjacencyGraphMatrix</em>.</p>
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147 <p>For a simple graph G with n vertices, the Siedal adjacency matrix for G is a n x n square matrix and
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148 its elements Mij are:</p>
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149 <div class="OptionsBox">
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150 . 0 if i == j
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151 <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj
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152 <br/> . 1 if i != j and vertex Vi is not adjacent to vertex Vj</div>
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153 </dd>
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154 <dt><strong><a name="getcolumnids" class="item"><strong>GetColumnIDs</strong></a></strong></dt>
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155 <dd>
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156 <div class="OptionsBox">
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157 @ColumnIDs = $GraphMatrix->GetColumnIDs();</div>
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158 <p>Returns an array containing any specified column IDs for <em>GraphMatrix</em>.</p>
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159 </dd>
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160 <dt><strong><a name="getmatrix" class="item"><strong>GetMatrix</strong></a></strong></dt>
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161 <dd>
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162 <div class="OptionsBox">
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163 $Matrix = $GraphMatrix->GetMatrix();</div>
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164 <p>Returns <em>Matrix</em> object corresponding to <em>GraphMatrix</em> object.</p>
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165 </dd>
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166 <dt><strong><a name="getmatrixtype" class="item"><strong>GetMatrixType</strong></a></strong></dt>
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167 <dd>
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168 <div class="OptionsBox">
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169 $MatrixType = $GraphMatrix->GetMatrixType();</div>
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170 <p>Returns <strong>MatrixType</strong> of <em>GraphMatrix</em>.</p>
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171 </dd>
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172 <dt><strong><a name="getrowids" class="item"><strong>GetRowIDs</strong></a></strong></dt>
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173 <dd>
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174 <div class="OptionsBox">
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175 @RowIDs = $GraphMatrix->GetRowIDs();</div>
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176 <p>Returns an array containing any specified rowIDs IDs for <em>GraphMatrix</em>.</p>
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177 </dd>
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178 <dt><strong><a name="stringifygraphmatrix" class="item"><strong>StringifyGraphMatrix</strong></a></strong></dt>
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179 <dd>
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180 <div class="OptionsBox">
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181 $String = $GraphMatrix->StringifyGraphMatrix();</div>
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182 <p>Returns a string containing information about <em>GraphMatrix</em> object.</p>
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183 </dd>
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184 </dl>
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185 <p>
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186 </p>
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187 <h2>AUTHOR</h2>
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188 <p><a href="mailto:msud@san.rr.com">Manish Sud</a></p>
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189 <p>
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190 </p>
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191 <h2>SEE ALSO</h2>
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192 <p><a href="./Constants.html">Constants.pm</a>, <a href="./Graph.html">Graph.pm</a>, <a href="./Matrix.html">Matrix.pm</a>
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193 </p>
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194 <p>
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195 </p>
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196 <h2>COPYRIGHT</h2>
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197 <p>Copyright (C) 2015 Manish Sud. All rights reserved.</p>
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198 <p>This file is part of MayaChemTools.</p>
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199 <p>MayaChemTools is free software; you can redistribute it and/or modify it under
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200 the terms of the GNU Lesser General Public License as published by the Free
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201 Software Foundation; either version 3 of the License, or (at your option)
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202 any later version.</p>
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203 <p> </p><p> </p><div class="DocNav">
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204 <table width="100%" border=0 cellpadding=0 cellspacing=2>
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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>
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206 </table>
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207 </div>
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208 <br />
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209 <center>
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210 <img src="../../images/h2o2.png">
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