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1 NAME
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2 GraphMatrix
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3
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4 SYNOPSIS
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5 use Graph::GraphMatrix;
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6
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7 use Graph::GraphMatrix qw(:all);
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8
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9 DESCRIPTION
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10 GraphMatrix class provides the following methods:
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11
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12 new, GenerateAdjacencyMatrix, GenerateAdmittanceMatrix,
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13 GenerateDegreeMatrix, GenerateDistanceMatrix, GenerateIncidenceMatrix,
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14 GenerateKirchhoffMatrix, GenerateLaplacianMatrix,
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15 GenerateNormalizedLaplacianMatrix, GenerateSiedelAdjacencyMatrix,
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16 GetColumnIDs, GetMatrix, GetMatrixType, GetRowIDs, StringifyGraphMatrix
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17
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18 METHODS
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19 new
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20 $NewGraphMatrix = new Graph::GraphMatrix($Graph);
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21
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22 Using specified *Graph*, new method creates a new GraphMatrix and
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23 returns newly created GraphMatrix.
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24
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25 GenerateAdjacencyMatrix
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26 $AdjacencyGraphMatrix = $GraphMatrix->GenerateAdjacencyMatrix();
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27
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28 Generates a new *AdjacencyGraphMatrix* for specified Graph and
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29 returns *AdjacencyGraphMatrix*.
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30
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31 For a simple graph G with n vertices, the adjacency matrix for G is
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32 a n x n square matrix and its elements Mij are:
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33
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34 . 0 if i == j
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35 . 1 if i != j and vertex Vi is adjacent to vertex Vj
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36 . 0 if i != j and vertex Vi is not adjacent to vertex Vj
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37
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38 GenerateAdmittanceMatrix
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39 $AdmittanceGraphMatrix = $GraphMatrix->GenerateAdmittanceMatrix();
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40
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41 Generates a new *AdmittanceGraphMatrix* for specified Graph and
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42 returns *AdmittanceGraphMatrix*.
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43
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44 AdmittanceMatrix is another name for LaplacianMatrix.
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45
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46 GenerateDegreeMatrix
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47 $DegreeGraphMatrix = $GraphMatrix->GenerateDegreeMatrix();
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48
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49 Generates a new *DegreeGraphMatrix* for specified Graph and returns
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50 *DegreeGraphMatrix*.
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51
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52 For a simple graph G with n vertices, the degree matrix for G is a n
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53 x n square matrix and its elements Mij are:
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54
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55 . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
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56 . 0 otherwise
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57
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58 GenerateDistanceMatrix
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59 $DistanceGraphMatrix = $GraphMatrix->GenerateDistanceMatrix();
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60
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61 Generates a new *DistanceGraphMatrix* for specified Graph using
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62 Floyd-Marshall algorithm [Ref 67] and returns *DistanceGraphMatrix*.
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63
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64 For a simple graph G with n vertices, the distance matrix for G is a
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65 n x n square matrix and its elements Mij are:
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66
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67 . 0 if i == j
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68 . d if i != j and d is the shortest distance between vertex Vi and vertex Vj
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69
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70 In the final matrix, value of constant BigNumber defined in
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71 Constants.pm module corresponds to vertices with no edges.
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72
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73 GenerateIncidenceMatrix
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74 $IncidenceGraphMatrix = $GraphMatrix->GenerateIncidenceMatrix();
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75
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76 Generates a new *IncidenceGraphMatrix* for specified Graph and
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77 returns *IncidenceGraphMatrix*.
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78
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79 For a simple graph G with n vertices and e edges, the incidence
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80 matrix for G is a n x e matrix its elements Mij are:
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81
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82 . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related
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83 . 0 otherwise
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84
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85 GenerateKirchhoffMatrix
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86 $KirchhoffGraphMatrix = $GraphMatrix->GenerateKirchhoffMatrix();
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87
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88 Generates a new *KirchhoffGraphMatrix* for specified Graph and
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89 returns *KirchhoffGraphMatrix*.
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90
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91 KirchhoffMatrix is another name for LaplacianMatrix.
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92
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93 GenerateLaplacianMatrix
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94 $LaplacianGraphMatrix = $GraphMatrix->GenerateLaplacianMatrix();
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95
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96 Generates a new *LaplacianGraphMatrix* for specified Graph and
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97 returns *LaplacianGraphMatrix*.
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98
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99 For a simple graph G with n vertices, the Laplacian matrix for G is
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100 a n x n square matrix and its elements Mij are:
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101
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102 . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
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103 . -1 if i != j and vertex Vi is adjacent to vertex Vj
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104 . 0 otherwise
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105
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106 The Laplacian matrix is the difference between the degree matrix and
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107 adjacency matrix.
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108
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109 GenerateNormalizedLaplacianMatrix
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110 $NormalizedLaplacianGraphMatrix = $GraphMatrix->GenerateNormalizedLaplacianMatrix();
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111
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112 Generates a new *NormalizedLaplacianGraphMatrix* for specified Graph
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113 and returns *NormalizedLaplacianGraphMatrix*.
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114
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115 For a simple graph G with n vertices, the normalized Laplacian
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116 matrix L for G is a n x n square matrix and its elements Lij are:
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117
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118 . 1 if i == j and deg(Vi) != 0
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119 . -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj
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120 . 0 otherwise
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121
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122 GenerateSiedelAdjacencyMatrix
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123 $SiedelAdjacencyGraphMatrix = $GraphMatrix->GenerateSiedelAdjacencyMatrix();
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124
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125 Generates a new *SiedelAdjacencyGraphMatrix* for specified Graph and
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126 returns *SiedelAdjacencyGraphMatrix*.
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127
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128 For a simple graph G with n vertices, the Siedal adjacency matrix
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129 for G is a n x n square matrix and its elements Mij are:
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130
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131 . 0 if i == j
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132 . -1 if i != j and vertex Vi is adjacent to vertex Vj
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133 . 1 if i != j and vertex Vi is not adjacent to vertex Vj
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134
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135 GetColumnIDs
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136 @ColumnIDs = $GraphMatrix->GetColumnIDs();
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137
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138 Returns an array containing any specified column IDs for
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139 *GraphMatrix*.
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140
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141 GetMatrix
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142 $Matrix = $GraphMatrix->GetMatrix();
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143
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144 Returns *Matrix* object corresponding to *GraphMatrix* object.
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145
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146 GetMatrixType
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147 $MatrixType = $GraphMatrix->GetMatrixType();
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148
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149 Returns MatrixType of *GraphMatrix*.
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150
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151 GetRowIDs
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152 @RowIDs = $GraphMatrix->GetRowIDs();
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153
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154 Returns an array containing any specified rowIDs IDs for
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155 *GraphMatrix*.
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156
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157 StringifyGraphMatrix
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158 $String = $GraphMatrix->StringifyGraphMatrix();
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159
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160 Returns a string containing information about *GraphMatrix* object.
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161
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162 AUTHOR
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163 Manish Sud <msud@san.rr.com>
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164
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165 SEE ALSO
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166 Constants.pm, Graph.pm, Matrix.pm
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167
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168 COPYRIGHT
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169 Copyright (C) 2015 Manish Sud. All rights reserved.
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170
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171 This file is part of MayaChemTools.
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172
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173 MayaChemTools is free software; you can redistribute it and/or modify it
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174 under the terms of the GNU Lesser General Public License as published by
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175 the Free Software Foundation; either version 3 of the License, or (at
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176 your option) any later version.
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177
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