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124 .\" ========================================================================
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125 .\"
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126 .IX Title "GRAPHMATRIX 1"
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127 .TH GRAPHMATRIX 1 "2015-03-29" "perl v5.14.2" "MayaChemTools"
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128 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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129 .\" way too many mistakes in technical documents.
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130 .if n .ad l
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131 .nh
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132 .SH "NAME"
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133 GraphMatrix
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134 .SH "SYNOPSIS"
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135 .IX Header "SYNOPSIS"
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136 use Graph::GraphMatrix;
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137 .PP
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138 use Graph::GraphMatrix qw(:all);
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139 .SH "DESCRIPTION"
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140 .IX Header "DESCRIPTION"
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141 \&\fBGraphMatrix\fR class provides the following methods:
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142 .PP
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143 new, GenerateAdjacencyMatrix, GenerateAdmittanceMatrix, GenerateDegreeMatrix,
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144 GenerateDistanceMatrix, GenerateIncidenceMatrix, GenerateKirchhoffMatrix,
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145 GenerateLaplacianMatrix, GenerateNormalizedLaplacianMatrix,
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146 GenerateSiedelAdjacencyMatrix, GetColumnIDs, GetMatrix, GetMatrixType, GetRowIDs,
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147 StringifyGraphMatrix
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148 .SS "\s-1METHODS\s0"
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149 .IX Subsection "METHODS"
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150 .IP "\fBnew\fR" 4
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151 .IX Item "new"
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152 .Vb 1
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153 \& $NewGraphMatrix = new Graph::GraphMatrix($Graph);
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154 .Ve
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155 .Sp
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156 Using specified \fIGraph\fR, \fBnew\fR method creates a new \fBGraphMatrix\fR and returns
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157 newly created \fBGraphMatrix\fR.
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158 .IP "\fBGenerateAdjacencyMatrix\fR" 4
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159 .IX Item "GenerateAdjacencyMatrix"
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160 .Vb 1
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161 \& $AdjacencyGraphMatrix = $GraphMatrix\->GenerateAdjacencyMatrix();
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162 .Ve
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163 .Sp
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164 Generates a new \fIAdjacencyGraphMatrix\fR for specified \fBGraph\fR and returns
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165 \&\fIAdjacencyGraphMatrix\fR.
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166 .Sp
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167 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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168 its elements Mij are:
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169 .Sp
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170 .Vb 3
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171 \& . 0 if i == j
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172 \& . 1 if i != j and vertex Vi is adjacent to vertex Vj
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173 \& . 0 if i != j and vertex Vi is not adjacent to vertex Vj
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174 .Ve
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175 .IP "\fBGenerateAdmittanceMatrix\fR" 4
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176 .IX Item "GenerateAdmittanceMatrix"
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177 .Vb 1
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178 \& $AdmittanceGraphMatrix = $GraphMatrix\->GenerateAdmittanceMatrix();
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179 .Ve
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180 .Sp
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181 Generates a new \fIAdmittanceGraphMatrix\fR for specified \fBGraph\fR and returns
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182 \&\fIAdmittanceGraphMatrix\fR.
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183 .Sp
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184 \&\fBAdmittanceMatrix\fR is another name for \fBLaplacianMatrix\fR.
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185 .IP "\fBGenerateDegreeMatrix\fR" 4
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186 .IX Item "GenerateDegreeMatrix"
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187 .Vb 1
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188 \& $DegreeGraphMatrix = $GraphMatrix\->GenerateDegreeMatrix();
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189 .Ve
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190 .Sp
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191 Generates a new \fIDegreeGraphMatrix\fR for specified \fBGraph\fR and returns
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192 \&\fIDegreeGraphMatrix\fR.
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193 .Sp
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194 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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195 its elements Mij are:
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196 .Sp
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197 .Vb 2
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198 \& . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
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199 \& . 0 otherwise
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200 .Ve
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201 .IP "\fBGenerateDistanceMatrix\fR" 4
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202 .IX Item "GenerateDistanceMatrix"
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203 .Vb 1
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204 \& $DistanceGraphMatrix = $GraphMatrix\->GenerateDistanceMatrix();
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205 .Ve
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206 .Sp
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207 Generates a new \fIDistanceGraphMatrix\fR for specified \fBGraph\fR using Floyd-Marshall
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208 algorithm [Ref 67] and returns \fIDistanceGraphMatrix\fR.
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209 .Sp
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210 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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211 its elements Mij are:
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212 .Sp
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213 .Vb 2
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214 \& . 0 if i == j
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215 \& . d if i != j and d is the shortest distance between vertex Vi and vertex Vj
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216 .Ve
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217 .Sp
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218 In the final matrix, value of constant \fBBigNumber\fR defined in \fBConstants.pm\fR module
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219 corresponds to vertices with no edges.
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220 .IP "\fBGenerateIncidenceMatrix\fR" 4
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221 .IX Item "GenerateIncidenceMatrix"
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222 .Vb 1
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223 \& $IncidenceGraphMatrix = $GraphMatrix\->GenerateIncidenceMatrix();
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224 .Ve
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225 .Sp
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226 Generates a new \fIIncidenceGraphMatrix\fR for specified \fBGraph\fR and returns
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227 \&\fIIncidenceGraphMatrix\fR.
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228 .Sp
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229 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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230 its elements Mij are:
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231 .Sp
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232 .Vb 2
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233 \& . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related
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234 \& . 0 otherwise
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235 .Ve
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236 .IP "\fBGenerateKirchhoffMatrix\fR" 4
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237 .IX Item "GenerateKirchhoffMatrix"
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238 .Vb 1
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239 \& $KirchhoffGraphMatrix = $GraphMatrix\->GenerateKirchhoffMatrix();
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240 .Ve
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241 .Sp
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242 Generates a new \fIKirchhoffGraphMatrix\fR for specified \fBGraph\fR and returns
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243 \&\fIKirchhoffGraphMatrix\fR.
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244 .Sp
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245 \&\fBKirchhoffMatrix\fR is another name for \fBLaplacianMatrix\fR.
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246 .IP "\fBGenerateLaplacianMatrix\fR" 4
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247 .IX Item "GenerateLaplacianMatrix"
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248 .Vb 1
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249 \& $LaplacianGraphMatrix = $GraphMatrix\->GenerateLaplacianMatrix();
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250 .Ve
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251 .Sp
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252 Generates a new \fILaplacianGraphMatrix\fR for specified \fBGraph\fR and returns
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253 \&\fILaplacianGraphMatrix\fR.
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254 .Sp
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255 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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256 its elements Mij are:
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257 .Sp
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258 .Vb 3
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259 \& . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
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260 \& . \-1 if i != j and vertex Vi is adjacent to vertex Vj
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261 \& . 0 otherwise
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262 .Ve
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263 .Sp
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264 The Laplacian matrix is the difference between the degree matrix and adjacency matrix.
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265 .IP "\fBGenerateNormalizedLaplacianMatrix\fR" 4
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266 .IX Item "GenerateNormalizedLaplacianMatrix"
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267 .Vb 1
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268 \& $NormalizedLaplacianGraphMatrix = $GraphMatrix\->GenerateNormalizedLaplacianMatrix();
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269 .Ve
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270 .Sp
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271 Generates a new \fINormalizedLaplacianGraphMatrix\fR for specified \fBGraph\fR and returns
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272 \&\fINormalizedLaplacianGraphMatrix\fR.
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273 .Sp
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274 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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275 matrix and its elements Lij are:
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276 .Sp
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277 .Vb 3
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278 \& . 1 if i == j and deg(Vi) != 0
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279 \& . \-1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj
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280 \& . 0 otherwise
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281 .Ve
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282 .IP "\fBGenerateSiedelAdjacencyMatrix\fR" 4
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283 .IX Item "GenerateSiedelAdjacencyMatrix"
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284 .Vb 1
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285 \& $SiedelAdjacencyGraphMatrix = $GraphMatrix\->GenerateSiedelAdjacencyMatrix();
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286 .Ve
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287 .Sp
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288 Generates a new \fISiedelAdjacencyGraphMatrix\fR for specified \fBGraph\fR and returns
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289 \&\fISiedelAdjacencyGraphMatrix\fR.
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290 .Sp
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291 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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292 its elements Mij are:
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293 .Sp
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294 .Vb 3
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295 \& . 0 if i == j
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296 \& . \-1 if i != j and vertex Vi is adjacent to vertex Vj
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297 \& . 1 if i != j and vertex Vi is not adjacent to vertex Vj
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298 .Ve
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299 .IP "\fBGetColumnIDs\fR" 4
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300 .IX Item "GetColumnIDs"
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301 .Vb 1
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302 \& @ColumnIDs = $GraphMatrix\->GetColumnIDs();
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303 .Ve
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304 .Sp
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305 Returns an array containing any specified column IDs for \fIGraphMatrix\fR.
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306 .IP "\fBGetMatrix\fR" 4
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307 .IX Item "GetMatrix"
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308 .Vb 1
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309 \& $Matrix = $GraphMatrix\->GetMatrix();
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310 .Ve
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311 .Sp
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312 Returns \fIMatrix\fR object corresponding to \fIGraphMatrix\fR object.
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313 .IP "\fBGetMatrixType\fR" 4
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314 .IX Item "GetMatrixType"
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315 .Vb 1
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316 \& $MatrixType = $GraphMatrix\->GetMatrixType();
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317 .Ve
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318 .Sp
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319 Returns \fBMatrixType\fR of \fIGraphMatrix\fR.
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320 .IP "\fBGetRowIDs\fR" 4
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321 .IX Item "GetRowIDs"
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322 .Vb 1
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323 \& @RowIDs = $GraphMatrix\->GetRowIDs();
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324 .Ve
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325 .Sp
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326 Returns an array containing any specified rowIDs IDs for \fIGraphMatrix\fR.
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327 .IP "\fBStringifyGraphMatrix\fR" 4
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328 .IX Item "StringifyGraphMatrix"
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329 .Vb 1
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330 \& $String = $GraphMatrix\->StringifyGraphMatrix();
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331 .Ve
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332 .Sp
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333 Returns a string containing information about \fIGraphMatrix\fR object.
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334 .SH "AUTHOR"
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335 .IX Header "AUTHOR"
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336 Manish Sud <msud@san.rr.com>
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337 .SH "SEE ALSO"
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338 .IX Header "SEE ALSO"
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339 Constants.pm, Graph.pm, Matrix.pm
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340 .SH "COPYRIGHT"
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341 .IX Header "COPYRIGHT"
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342 Copyright (C) 2015 Manish Sud. All rights reserved.
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343 .PP
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344 This file is part of MayaChemTools.
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345 .PP
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346 MayaChemTools is free software; you can redistribute it and/or modify it under
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347 the terms of the \s-1GNU\s0 Lesser General Public License as published by the Free
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348 Software Foundation; either version 3 of the License, or (at your option)
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349 any later version.
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