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NAME

GraphMatrix

SYNOPSIS

use Graph::GraphMatrix;

use Graph::GraphMatrix qw(:all);

DESCRIPTION

GraphMatrix class provides the following methods:

new, GenerateAdjacencyMatrix, GenerateAdmittanceMatrix, GenerateDegreeMatrix, GenerateDistanceMatrix, GenerateIncidenceMatrix, GenerateKirchhoffMatrix, GenerateLaplacianMatrix, GenerateNormalizedLaplacianMatrix, GenerateSiedelAdjacencyMatrix, GetColumnIDs, GetMatrix, GetMatrixType, GetRowIDs, StringifyGraphMatrix

METHODS

new

$NewGraphMatrix = new Graph::GraphMatrix($Graph);

Using specified Graph, new method creates a new GraphMatrix and returns newly created GraphMatrix.

GenerateAdjacencyMatrix

$AdjacencyGraphMatrix = $GraphMatrix->GenerateAdjacencyMatrix();

Generates a new AdjacencyGraphMatrix for specified Graph and returns AdjacencyGraphMatrix.

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:

. 0 if i == j
. 1 if i != j and vertex Vi is adjacent to vertex Vj
. 0 if i != j and vertex Vi is not adjacent to vertex Vj

GenerateAdmittanceMatrix

$AdmittanceGraphMatrix = $GraphMatrix->GenerateAdmittanceMatrix();

Generates a new AdmittanceGraphMatrix for specified Graph and returns AdmittanceGraphMatrix.

AdmittanceMatrix is another name for LaplacianMatrix.

GenerateDegreeMatrix

$DegreeGraphMatrix = $GraphMatrix->GenerateDegreeMatrix();

Generates a new DegreeGraphMatrix for specified Graph and returns DegreeGraphMatrix.

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:

. deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
. 0 otherwise

GenerateDistanceMatrix

$DistanceGraphMatrix = $GraphMatrix->GenerateDistanceMatrix();

Generates a new DistanceGraphMatrix for specified Graph using Floyd-Marshall algorithm [Ref 67] and returns DistanceGraphMatrix.

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:

. 0 if i == j
. d if i != j and d is the shortest distance between vertex Vi and vertex Vj

In the final matrix, value of constant BigNumber defined in Constants.pm module corresponds to vertices with no edges.

GenerateIncidenceMatrix

$IncidenceGraphMatrix = $GraphMatrix->GenerateIncidenceMatrix();

Generates a new IncidenceGraphMatrix for specified Graph and returns IncidenceGraphMatrix.

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:

. 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related
. 0 otherwise

GenerateKirchhoffMatrix

$KirchhoffGraphMatrix = $GraphMatrix->GenerateKirchhoffMatrix();

Generates a new KirchhoffGraphMatrix for specified Graph and returns KirchhoffGraphMatrix.

KirchhoffMatrix is another name for LaplacianMatrix.

GenerateLaplacianMatrix

$LaplacianGraphMatrix = $GraphMatrix->GenerateLaplacianMatrix();

Generates a new LaplacianGraphMatrix for specified Graph and returns LaplacianGraphMatrix.

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:

. deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi
. -1 if i != j and vertex Vi is adjacent to vertex Vj
. 0 otherwise

The Laplacian matrix is the difference between the degree matrix and adjacency matrix.

GenerateNormalizedLaplacianMatrix

$NormalizedLaplacianGraphMatrix = $GraphMatrix->GenerateNormalizedLaplacianMatrix();

Generates a new NormalizedLaplacianGraphMatrix for specified Graph and returns NormalizedLaplacianGraphMatrix.

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:

. 1 if i == j and deg(Vi) != 0
. -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj
. 0 otherwise

GenerateSiedelAdjacencyMatrix

$SiedelAdjacencyGraphMatrix = $GraphMatrix->GenerateSiedelAdjacencyMatrix();

Generates a new SiedelAdjacencyGraphMatrix for specified Graph and returns SiedelAdjacencyGraphMatrix.

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:

. 0 if i == j
. -1 if i != j and vertex Vi is adjacent to vertex Vj
. 1 if i != j and vertex Vi is not adjacent to vertex Vj

GetColumnIDs

@ColumnIDs = $GraphMatrix->GetColumnIDs();

Returns an array containing any specified column IDs for GraphMatrix.

GetMatrix

$Matrix = $GraphMatrix->GetMatrix();

Returns Matrix object corresponding to GraphMatrix object.

GetMatrixType

$MatrixType = $GraphMatrix->GetMatrixType();

Returns MatrixType of GraphMatrix.

GetRowIDs

@RowIDs = $GraphMatrix->GetRowIDs();

Returns an array containing any specified rowIDs IDs for GraphMatrix.

StringifyGraphMatrix

$String = $GraphMatrix->StringifyGraphMatrix();

Returns a string containing information about GraphMatrix object.

AUTHOR

Manish Sud

SEE ALSO

Constants.pm, Graph.pm, Matrix.pm

COPYRIGHT

Copyright (C) 2024 Manish Sud. All rights reserved.

This file is part of MayaChemTools.

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.