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<html> <head> <title>MayaChemTools:Documentation:Graph.pm</title> <meta http-equiv="content-type" content="text/html;charset=utf-8"> <link rel="stylesheet" type="text/css" href="../../css/MayaChemTools.css"> </head> <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10"> <br/> <center> <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a> </center> <br/> <div class="DocNav"> <table width="100%" border=0 cellpadding=0 cellspacing=2> <tr align="left" valign="top"><td width="33%" align="left"><a href="./PathsTraversal.html" title="PathsTraversal.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./HTMLUtil.html" title="HTMLUtil.html">Next</a></td><td width="34%" align="middle"><strong>Graph.pm</strong></td><td width="33%" align="right"><a href="././code/Graph.html" title="View source code">Code</a> | <a href="./../pdf/Graph.pdf" title="PDF US Letter Size">PDF</a> | <a href="./../pdfgreen/Graph.pdf" title="PDF US Letter Size with narrow margins: www.changethemargins.com">PDFGreen</a> | <a href="./../pdfa4/Graph.pdf" title="PDF A4 Size">PDFA4</a> | <a href="./../pdfa4green/Graph.pdf" title="PDF A4 Size with narrow margins: www.changethemargins.com">PDFA4Green</a></td></tr> </table> </div> <p> </p> <h2>NAME</h2> <p>Graph</p> <p> </p> <h2>SYNOPSIS</h2> <p>use Graph;</p> <p>use Graph qw(:all);</p> <p> </p> <h2>DESCRIPTION</h2> <p><strong>Graph</strong> class provides the following methods:</p> <p> <a href="#new">new</a>, <a href="#addcycle">AddCycle</a>, <a href="#addedge">AddEdge</a>, <a href="#addedges">AddEdges</a>, <a href="#addpath">AddPath</a>, <a href="#addvertex">AddVertex</a>, <a href="#addvertices">AddVertices</a>, <a href="#clearcycles">ClearCycles</a> , <a href="#copy">Copy</a>, <a href="#copyedgesproperties">CopyEdgesProperties</a>, <a href="#copyverticesandedges">CopyVerticesAndEdges</a>, <a href="#copyverticesproperties">CopyVerticesProperties</a> , <a href="#deletecycle">DeleteCycle</a>, <a href="#deleteedge">DeleteEdge</a>, <a href="#deleteedgeproperties">DeleteEdgeProperties</a>, <a href="#deleteedgeproperty">DeleteEdgeProperty</a>, <a href="#deleteedges">DeleteEdges</a> , <a href="#deleteedgesproperties">DeleteEdgesProperties</a>, <a href="#deleteedgesproperty">DeleteEdgesProperty</a>, <a href="#deletegraphproperties">DeleteGraphProperties</a> , <a href="#deletegraphproperty">DeleteGraphProperty</a>, <a href="#deletepath">DeletePath</a>, <a href="#deletevertex">DeleteVertex</a>, <a href="#deletevertexproperties">DeleteVertexProperties</a> , <a href="#deletevertexproperty">DeleteVertexProperty</a>, <a href="#deletevertices">DeleteVertices</a>, <a href="#deleteverticesproperty">DeleteVerticesProperty</a>, <a href="#detectcycles">DetectCycles</a> , <a href="#getadjacencymatrix">GetAdjacencyMatrix</a>, <a href="#getadmittancematrix">GetAdmittanceMatrix</a>, <a href="#getallpaths">GetAllPaths</a>, <a href="#getallpathsstartingat">GetAllPathsStartingAt</a> , <a href="#getallpathsstartingatwithlength">GetAllPathsStartingAtWithLength</a>, <a href="#getallpathsstartingatwithlengthupto">GetAllPathsStartingAtWithLengthUpto</a> , <a href="#getallpathswithlength">GetAllPathsWithLength</a>, <a href="#getallpathswithlengthupto">GetAllPathsWithLengthUpto</a>, <a href="#getcircumference">GetCircumference</a> , <a href="#getconnectedcomponentsvertices">GetConnectedComponentsVertices</a>, <a href="#getcycles">GetCycles</a>, <a href="#getcycleswithevensize">GetCyclesWithEvenSize</a> , <a href="#getcycleswithoddsize">GetCyclesWithOddSize</a>, <a href="#getcycleswithsize">GetCyclesWithSize</a>, <a href="#getcycleswithsizegreaterthan">GetCyclesWithSizeGreaterThan</a> , <a href="#getcycleswithsizelessthan">GetCyclesWithSizeLessThan</a>, <a href="#getdegree">GetDegree</a>, <a href="#getdegreematrix">GetDegreeMatrix</a>, <a href="#getdistancematrix">GetDistanceMatrix</a> , <a href="#getedgecycles">GetEdgeCycles</a>, <a href="#getedgecycleswithevensize">GetEdgeCyclesWithEvenSize</a>, <a href="#getedgecycleswithoddsize">GetEdgeCyclesWithOddSize</a> , <a href="#getedgecycleswithsize">GetEdgeCyclesWithSize</a>, <a href="#getedgecycleswithsizegreaterthan">GetEdgeCyclesWithSizeGreaterThan</a> , <a href="#getedgecycleswithsizelessthan">GetEdgeCyclesWithSizeLessThan</a>, <a href="#getedgeproperties">GetEdgeProperties</a>, <a href="#getedgeproperty">GetEdgeProperty</a>, <a href="#getedges">GetEdges</a> , <a href="#getedgesproperty">GetEdgesProperty</a>, <a href="#getfusedandnonfusedcycles">GetFusedAndNonFusedCycles</a>, <a href="#getgirth">GetGirth</a>, <a href="#getgraphproperties">GetGraphProperties</a> , <a href="#getgraphproperty">GetGraphProperty</a>, <a href="#getincidencematrix">GetIncidenceMatrix</a>, <a href="#getisolatedvertices">GetIsolatedVertices</a>, <a href="#getkirchhoffmatrix">GetKirchhoffMatrix</a> , <a href="#getlaplacianmatrix">GetLaplacianMatrix</a>, <a href="#getlargestcycle">GetLargestCycle</a>, <a href="#getlargestedgecycle">GetLargestEdgeCycle</a>, <a href="#getlargestvertexcycle">GetLargestVertexCycle</a> , <a href="#getleafvertices">GetLeafVertices</a>, <a href="#getmaximumdegree">GetMaximumDegree</a>, <a href="#getmininumdegree">GetMininumDegree</a>, <a href="#getneighborhoodvertices">GetNeighborhoodVertices</a> , <a href="#getneighborhoodverticeswithradiusupto">GetNeighborhoodVerticesWithRadiusUpto</a>, <a href="#getneighborhoodverticeswithsuccessors">GetNeighborhoodVerticesWithSuccessors</a> , <a href="#getneighborhoodverticeswithsuccessorsandradiusupto">GetNeighborhoodVerticesWithSuccessorsAndRadiusUpto</a>, <a href="#getneighbors">GetNeighbors</a> , <a href="#getnormalizedlaplacianmatrix">GetNormalizedLaplacianMatrix</a>, <a href="#getnumofcycles">GetNumOfCycles</a>, <a href="#getnumofcycleswithevensize">GetNumOfCyclesWithEvenSize</a> , <a href="#getnumofcycleswithoddsize">GetNumOfCyclesWithOddSize</a>, <a href="#getnumofcycleswithsize">GetNumOfCyclesWithSize</a> , <a href="#getnumofcycleswithsizegreaterthan">GetNumOfCyclesWithSizeGreaterThan</a>, <a href="#getnumofcycleswithsizelessthan">GetNumOfCyclesWithSizeLessThan</a> , <a href="#getnumofedgecycles">GetNumOfEdgeCycles</a>, <a href="#getnumofedgecycleswithevensize">GetNumOfEdgeCyclesWithEvenSize</a>, <a href="#getnumofedgecycleswithoddsize">GetNumOfEdgeCyclesWithOddSize</a> , <a href="#getnumofedgecycleswithsize">GetNumOfEdgeCyclesWithSize</a>, <a href="#getnumofedgecycleswithsizegreaterthan">GetNumOfEdgeCyclesWithSizeGreaterThan</a> , <a href="#getnumofedgecycleswithsizelessthan">GetNumOfEdgeCyclesWithSizeLessThan</a>, <a href="#getnumofvertexcycles">GetNumOfVertexCycles</a> , <a href="#getnumofvertexcycleswithevensize">GetNumOfVertexCyclesWithEvenSize</a>, <a href="#getnumofvertexcycleswithoddsize">GetNumOfVertexCyclesWithOddSize</a> , <a href="#getnumofvertexcycleswithsize">GetNumOfVertexCyclesWithSize</a>, <a href="#getnumofvertexcycleswithsizegreaterthan">GetNumOfVertexCyclesWithSizeGreaterThan</a> , <a href="#getnumofvertexcycleswithsizelessthan">GetNumOfVertexCyclesWithSizeLessThan</a>, <a href="#getpaths">GetPaths</a>, <a href="#getpathsbetween">GetPathsBetween</a> , <a href="#getpathsstartingat">GetPathsStartingAt</a>, <a href="#getpathsstartingatwithlength">GetPathsStartingAtWithLength</a> , <a href="#getpathsstartingatwithlengthupto">GetPathsStartingAtWithLengthUpto</a>, <a href="#getpathswithlength">GetPathsWithLength</a>, <a href="#getpathswithlengthupto">GetPathsWithLengthUpto</a> , <a href="#getsiedeladjacencymatrix">GetSiedelAdjacencyMatrix</a>, <a href="#getsizeoflargestcycle">GetSizeOfLargestCycle</a>, <a href="#getsizeoflargestedgecycle">GetSizeOfLargestEdgeCycle</a> , <a href="#getsizeoflargestvertexcycle">GetSizeOfLargestVertexCycle</a>, <a href="#getsizeofsmallestcycle">GetSizeOfSmallestCycle</a>, <a href="#getsizeofsmallestedgecycle">GetSizeOfSmallestEdgeCycle</a> , <a href="#getsizeofsmallestvertexcycle">GetSizeOfSmallestVertexCycle</a>, <a href="#getsmallestcycle">GetSmallestCycle</a>, <a href="#getsmallestedgecycle">GetSmallestEdgeCycle</a> , <a href="#getsmallestvertexcycle">GetSmallestVertexCycle</a>, <a href="#gettopologicallysortedvertices">GetTopologicallySortedVertices</a>, <a href="#getvertex">GetVertex</a> , <a href="#getvertexcycles">GetVertexCycles</a>, <a href="#getvertexcycleswithevensize">GetVertexCyclesWithEvenSize</a>, <a href="#getvertexcycleswithoddsize">GetVertexCyclesWithOddSize</a> , <a href="#getvertexcycleswithsize">GetVertexCyclesWithSize</a>, <a href="#getvertexcycleswithsizegreaterthan">GetVertexCyclesWithSizeGreaterThan</a> , <a href="#getvertexcycleswithsizelessthan">GetVertexCyclesWithSizeLessThan</a>, <a href="#getvertexproperties">GetVertexProperties</a>, <a href="#getvertexproperty">GetVertexProperty</a> , <a href="#getvertexwithlargestdegree">GetVertexWithLargestDegree</a>, <a href="#getvertexwithsmallestdegree">GetVertexWithSmallestDegree</a>, <a href="#getvertices">GetVertices</a> , <a href="#getverticesproperty">GetVerticesProperty</a>, <a href="#getverticeswithdegreelessthan">GetVerticesWithDegreeLessThan</a>, <a href="#hascycle">HasCycle</a>, <a href="#hasedge">HasEdge</a> , <a href="#hasedgeproperty">HasEdgeProperty</a>, <a href="#hasedges">HasEdges</a>, <a href="#hasfusedcycles">HasFusedCycles</a>, <a href="#hasgraphproperty">HasGraphProperty</a>, <a href="#haspath">HasPath</a>, <a href="#hasvertex">HasVertex</a> , <a href="#hasvertexproperty">HasVertexProperty</a>, <a href="#hasvertices">HasVertices</a>, <a href="#isacyclic">IsAcyclic</a>, <a href="#isacyclicedge">IsAcyclicEdge</a>, <a href="#isacyclicvertex">IsAcyclicVertex</a> , <a href="#iscyclic">IsCyclic</a>, <a href="#iscyclicedge">IsCyclicEdge</a>, <a href="#iscyclicvertex">IsCyclicVertex</a>, <a href="#isgraph">IsGraph</a>, <a href="#isisolatedvertex">IsIsolatedVertex</a>, <a href="#isleafvertex">IsLeafVertex</a> , <a href="#isunicyclic">IsUnicyclic</a>, <a href="#isunicyclicedge">IsUnicyclicEdge</a>, <a href="#isunicyclicvertex">IsUnicyclicVertex</a>, <a href="#setactivecyclicpaths">SetActiveCyclicPaths</a> , <a href="#setedgeproperties">SetEdgeProperties</a>, <a href="#setedgeproperty">SetEdgeProperty</a>, <a href="#setedgesproperty">SetEdgesProperty</a>, <a href="#setgraphproperties">SetGraphProperties</a> , <a href="#setgraphproperty">SetGraphProperty</a>, <a href="#setvertexproperties">SetVertexProperties</a>, <a href="#setvertexproperty">SetVertexProperty</a>, <a href="#setverticesproperty">SetVerticesProperty</a> , <a href="#stringifyedgesproperties">StringifyEdgesProperties</a>, <a href="#stringifygraph">StringifyGraph</a>, <a href="#stringifygraphproperties">StringifyGraphProperties</a> , <a href="#stringifyproperties">StringifyProperties</a>, <a href="#stringifyverticesandedges">StringifyVerticesAndEdges</a>, <a href="#stringifyverticesproperties">StringifyVerticesProperties</a> , <a href="#updateedgeproperty">UpdateEdgeProperty</a>, <a href="#updatevertexproperty">UpdateVertexProperty</a> </p><p> </p> <h2>METHODS</h2> <dl> <dt><strong><a name="new" class="item"><strong>new</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NewGraph = new Graph([@VertexIDs]);</div> <p>Using specified <em>Graph</em> <em>VertexIDs</em>, <strong>new</strong> method creates a new <strong>Graph</strong> object and returns newly created <strong>Graph</strong> object.</p> <p>Examples:</p> <div class="OptionsBox"> $Graph = new Graph(); <br/> $Graph = new Graph(@VertexIDs);</div> </dd> <dt><strong><a name="addcycle" class="item"><strong>AddCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->AddCycle(@VertexIDs);</div> <p>Adds edges between successive pair of <em>VertexIDs</em> including an additional edge from the last to first vertex ID to complete the cycle to <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="addedge" class="item"><strong>AddEdge</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->AddEdge($VertexID1, $VertexID2);</div> <p>Adds an edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="addedges" class="item"><strong>AddEdges</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->AddEdges(@VertexIDs);</div> <p>Adds edges between successive pair of <em>VertexIDs</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="addpath" class="item"><strong>AddPath</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->AddPath(@VertexIDs);</div> <p>Adds edges between successive pair of <em>VertexIDs</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="addvertex" class="item"><strong>AddVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->AddVertex($VertexID);</div> <p>Adds <em>VertexID</em> to <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="addvertices" class="item"><strong>AddVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->AddVertices(@VertexIDs);</div> <p>Adds vertices using <em>VertexIDs</em> to <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="clearcycles" class="item"><strong>ClearCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->ClearCycles();</div> <p>Delete all cycle properties assigned to graph, vertices, and edges by <em>DetectCycles</em> method.</p> </dd> <dt><strong><a name="copy" class="item"><strong>Copy</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NewGraph = $Graph->Copy();</div> <p>Copies <em>Graph</em> and its associated data using <strong>Storable::dclone</strong> and returns a new <strong>Graph</strong> object.</p> </dd> <dt><strong><a name="copyedgesproperties" class="item"><strong>CopyEdgesProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $OtherGraph = $Graph->CopyEdgesProperties($OtherGraph);</div> <p>Copies all properties associated with edges from <em>Graph</em> to <em>$OtherGraph</em> and returns <em>OtherGraph</em>.</p> </dd> <dt><strong><a name="copyverticesandedges" class="item"><strong>CopyVerticesAndEdges</strong></a></strong></dt> <dd> <div class="OptionsBox"> $OtherGraph = $Graph->CopyVerticesAndEdges($OtherGraph);</div> <p>Copies all vertices and edges from <em>Graph</em> to <em>$OtherGraph</em> and returns <em>OtherGraph</em>.</p> </dd> <dt><strong><a name="copyverticesproperties" class="item"><strong>CopyVerticesProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $OtherGraph = $Graph->CopyVerticesProperties($OtherGraph);</div> <p>Copies all properties associated with vertices from <em>Graph</em> to <em>$OtherGraph</em> and returns <em>OtherGraph</em>.</p> </dd> <dt><strong><a name="deletecycle" class="item"><strong>DeleteCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteCycle(@VertexIDs);</div> <p>Deletes edges between successive pair of <em>VertexIDs</em> including an additional edge from the last to first vertex ID to complete the cycle to <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deleteedge" class="item"><strong>DeleteEdge</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteEdge($VertexID1, $VertexID2);</div> <p>Deletes an edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deleteedgeproperties" class="item"><strong>DeleteEdgeProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteEdgeProperties($VertexID1, $VertexID2);</div> <p>Deletes all properties associated with edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deleteedgeproperty" class="item"><strong>DeleteEdgeProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteEdgeProperty($PropertyName, $VertexID1, $VertexID2);</div> <p>Deletes <em>PropertyName</em> associated with edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deleteedges" class="item"><strong>DeleteEdges</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteEdges(@VertexIDs);</div> <p>Deletes edges between successive pair of <em>VertexIDs</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deleteedgesproperties" class="item"><strong>DeleteEdgesProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteEdgesProperties(@VertexIDs);</div> <p>Deletes all properties associated with edges between successive pair of <em>VertexIDs</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deleteedgesproperty" class="item"><strong>DeleteEdgesProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteEdgesProperty($PropertyName, @VertexIDs);</div> <p>Deletes <em>PropertyName</em> associated with edges between successive pair of <em>VertexIDs</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deletegraphproperties" class="item"><strong>DeleteGraphProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteGraphProperties();</div> <p>Deletes all properties associated as graph not including properties associated to vertices or edges and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deletegraphproperty" class="item"><strong>DeleteGraphProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteGraphProperty($PropertyName);</div> <p>Deletes a <em>PropertyName</em> associated as graph property and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deletepath" class="item"><strong>DeletePath</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeletePath(@VertexIDs);</div> <p>Deletes edges between successive pair of <em>VertexIDs</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deletevertex" class="item"><strong>DeleteVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteVertex($VertexID);</div> <p>Deletes <em>VertexID</em> to <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deletevertexproperties" class="item"><strong>DeleteVertexProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteVertexProperties($VertexID);</div> <p>Deletes all properties associated with <em>VertexID</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deletevertexproperty" class="item"><strong>DeleteVertexProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteVertexProperty($PropertyName, $VertexID);</div> <p>Deletes a <em>PropertyName</em> associated with <em>VertexID</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deletevertices" class="item"><strong>DeleteVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteVertices(@VertexIDs);</div> <p>Deletes vertices specified in <em>VertexIDs</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="deleteverticesproperty" class="item"><strong>DeleteVerticesProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DeleteVerticesProperty($PropertyName, @VertexIDs);</div> <p>Deletes a <em>PropertyName</em> associated with <em>VertexIDs</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="detectcycles" class="item"><strong>DetectCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->DetectCycles();</div> <p>Detect cycles using <strong>CyclesDetection</strong> class and associate found cycles to <em>Graph</em> object as graph properties: <em>ActiveCyclicPaths, AllCyclicPaths, IndependentCyclicPaths</em>.</p> <p>Notes:</p> <div class="OptionsBox"> . CyclesDetection class detects all cycles in the graph and filters them to find independent cycles. <br/> . All cycles related methods in the graph operate on ActiveCyclicPaths. By default, active cyclic paths correspond to IndependentCyclicPaths. This behavior can be changed using SetActiveCyclicPaths method.</div> </dd> <dt><strong><a name="getadjacencymatrix" class="item"><strong>GetAdjacencyMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetAdjacencyMatrix();</div> <p>Returns adjacency matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . 0 if i == j <br/> . 1 if i != j and vertex Vi is adjacent to vertex Vj <br/> . 0 if i != j and vertex Vi is not adjacent to vertex Vj</div> </dd> <dt><strong><a name="getadmittancematrix" class="item"><strong>GetAdmittanceMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetAdmittanceMatrix();</div> <p>Returns admittance matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . 0 if i == j <br/> . 1 if i != j and vertex Vi is adjacent to vertex Vj <br/> . 0 if i != j and vertex Vi is not adjacent to vertex Vj</div> </dd> <dt><strong><a name="getallpaths" class="item"><strong>GetAllPaths</strong></a></strong></dt> <dd> <div class="OptionsBox"> $PathsRef = $Graph->GetAllPaths([$AllowCycles]);</div> <p>Returns a reference to an array containing <strong>Path</strong> objects corresponding to all possible lengths starting from each vertex in graph with sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle. Duplicate paths are not removed.</p> </dd> <dt><strong><a name="getallpathsstartingat" class="item"><strong>GetAllPathsStartingAt</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->GetAllPathsStartingAt($StartVertexID, [$AllowCycles]);</div> <p>Returns an array of <em>Path</em> objects starting from a <em>StartVertexID</em> of any length with sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getallpathsstartingatwithlength" class="item"><strong>GetAllPathsStartingAtWithLength</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->GetAllPathsStartingAtWithLength($StartVertexID, $Length, [$AllowCycles]);</div> <p>Returns an array of <em>Path</em> objects starting from a <em>StartVertexID</em> of specified <em>Length</em> with sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getallpathsstartingatwithlengthupto" class="item"><strong>GetAllPathsStartingAtWithLengthUpto</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->GetAllPathsStartingAtWithLengthUpto($StartVertexID, $Length, [$AllowCycles]);</div> <p>Returns an array of <em>Path</em> objects starting from a <em>StartVertexID</em> with length upto a <em>Length</em> with sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getallpathswithlength" class="item"><strong>GetAllPathsWithLength</strong></a></strong></dt> <dd> <div class="OptionsBox"> $PathsRef = $Graph->GetAllPathsWithLength($Length, [$AllowCycles]);</div> <p>Returns a reference to an array containing <strong>Path</strong> objects corresponding to paths with <em>Length</em> starting from each vertex in graph with sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle. Duplicate paths are not removed.</p> </dd> <dt><strong><a name="getallpathswithlengthupto" class="item"><strong>GetAllPathsWithLengthUpto</strong></a></strong></dt> <dd> <div class="OptionsBox"> $PathsRef = $Graph->GetAllPathsWithLengthUpto($Length, [$AllowCycles]);</div> <p>Returns a reference to an array containing <strong>Path</strong> objects corresponding to paths up to specified <em>Length</em> starting from each vertex in graph with sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle. Duplicate paths are not removed.</p> </dd> <dt><strong><a name="getcircumference" class="item"><strong>GetCircumference</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Circumference = $Graph->GetCircumference();</div> <p>Returns size of largest cycle in a <em>Graph</em></p> </dd> <dt><strong><a name="getconnectedcomponentsvertices" class="item"><strong>GetConnectedComponentsVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> @ConnectedComponents = $Graph->GetConnectedComponentsVertices();</div> <p>Returns an array <em>ConnectedComponents</em> containing referecens to arrays with vertex IDs for each component sorted in order of their decreasing size.</p> </dd> <dt><strong><a name="getcycles" class="item"><strong>GetCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graphs->GetCycles();</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getcycleswithevensize" class="item"><strong>GetCyclesWithEvenSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetCyclesWithEvenSize();</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with even size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getcycleswithoddsize" class="item"><strong>GetCyclesWithOddSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetCyclesWithOddSize();</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with odd size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getcycleswithsize" class="item"><strong>GetCyclesWithSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetCyclesWithSize($CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with <em>CycleSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getcycleswithsizegreaterthan" class="item"><strong>GetCyclesWithSizeGreaterThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetCyclesWithSizeGreaterThan($CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size greater than <em>CycleSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getcycleswithsizelessthan" class="item"><strong>GetCyclesWithSizeLessThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetCyclesWithSizeGreaterThan($CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size less than <em>CycleSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getdegree" class="item"><strong>GetDegree</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Degree = $Graph->GetDegree($VertexID);</div> <p>Returns <strong>Degree</strong> for <em>VertexID</em> in a <em>Graph</em> corresponding to sum of in and out vertex degree values.</p> </dd> <dt><strong><a name="getdegreematrix" class="item"><strong>GetDegreeMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetDegreeMatrix();</div> <p>Returns degree matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi <br/> . 0 otherwise</div> </dd> <dt><strong><a name="getdistancematrix" class="item"><strong>GetDistanceMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetDistanceMatrix();</div> <p>Returns distance matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . 0 if i == j <br/> . d if i != j and d is the shortest distance between vertex Vi and vertex Vj</div> <p>In the final matrix, value of constant <strong>BigNumber</strong> defined in <strong>Constants.pm</strong> module corresponds to vertices with no edges.</p> </dd> <dt><strong><a name="getedgecycles" class="item"><strong>GetEdgeCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetEdgeCycles($VertexID1, $VertexID2);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to all cycles containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedgecycleswithevensize" class="item"><strong>GetEdgeCyclesWithEvenSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetEdgeCyclesWithEvenSize($VertexID1, $VertexID2);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with even size containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedgecycleswithoddsize" class="item"><strong>GetEdgeCyclesWithOddSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetEdgeCyclesWithOddSize($VertexID1, $VertexID2);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with odd size containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedgecycleswithsize" class="item"><strong>GetEdgeCyclesWithSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetEdgeCyclesWithSize($VertexID1, $VertexID2, $CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size <em>CycleSize</em> containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedgecycleswithsizegreaterthan" class="item"><strong>GetEdgeCyclesWithSizeGreaterThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetEdgeCyclesWithSizeGreaterThan($VertexID1, $VertexID2, $CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size greater than <em>CycleSize</em> containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedgecycleswithsizelessthan" class="item"><strong>GetEdgeCyclesWithSizeLessThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetEdgeCyclesWithSizeLessThan($VertexID1, $VertexID2, $CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size less than <em>CycleSize</em> containing edge between <em>VertexID1</em> and <em>VertexID2</em>.</p> </dd> <dt><strong><a name="getedgeproperties" class="item"><strong>GetEdgeProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> %EdgeProperties = $Graph->GetEdgeProperties($VertexID1, $VertexID2);</div> <p>Returns a hash <strong>EdgeProperties</strong> containing all <strong>PropertyName</strong> and <strong>PropertyValue</strong> pairs associated with an edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedgeproperty" class="item"><strong>GetEdgeProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Value = $Graph->GetEdgeProperty($PropertyName, $VertexID1, $VertexID2);</div> <p>Returns value of <em>PropertyName</em> associated with an edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedges" class="item"><strong>GetEdges</strong></a></strong></dt> <dd> <div class="OptionsBox"> @EdgeVertexIDs = $Graph->GetEdges($VertexID); <br/> $NumOfEdges = $Graph->GetEdges($VertexID);</div> <p>Returns an array <em>EdgeVertexIDs</em> with successive pair of IDs corresponding to edges involving <em>VertexID</em> or number of edges for <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getedgesproperty" class="item"><strong>GetEdgesProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> @PropertyValues = $Graph->GetEdgesProperty($PropertyName, @VertexIDs);</div> <p>Returns an array <em>PropertyValues</em> containing property values corresponding to <em>PropertyName</em> associated with edges between successive pair of <em>VertexIDs</em>.</p> </dd> <dt><strong><a name="getfusedandnonfusedcycles" class="item"><strong>GetFusedAndNonFusedCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> ($FusedCycleSetsRef, $NonFusedCyclesRef) = $Graph->GetFusedAndNonFusedCycles();</div> <p>Returns references to arrays <em>FusedCycleSetsRef</em> and <em>NonFusedCyclesRef</em> containing references to arrays of cyclic <em>Path</em> objects corresponding to fuses and non-fused cyclic paths.</p> </dd> <dt><strong><a name="getgirth" class="item"><strong>GetGirth</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Girth = $Graph->GetGirth();</div> <p>Returns size of smallest cycle in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getgraphproperties" class="item"><strong>GetGraphProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> %GraphProperties = $Graph->GetGraphProperties();</div> <p>Returns a hash <strong>EdgeProperties</strong> containing all <strong>PropertyName</strong> and <strong>PropertyValue</strong> pairs associated with graph in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getgraphproperty" class="item"><strong>GetGraphProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $PropertyValue = $Graph->GetGraphProperty($PropertyName);</div> <p>Returns value of <em>PropertyName</em> associated with graph in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getincidencematrix" class="item"><strong>GetIncidenceMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetIncidenceMatrix();</div> <p>Returns incidence matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . 1 if vertex Vi and the edge Ej are incident; in other words, Vi and Ej are related <br/> . 0 otherwise</div> </dd> <dt><strong><a name="getisolatedvertices" class="item"><strong>GetIsolatedVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexIDs = $Graph->GetIsolatedVertices();</div> <p>Returns an array <em>VertexIDs</em> containing vertices without any edges in <em>Graph</em>.</p> </dd> <dt><strong><a name="getkirchhoffmatrix" class="item"><strong>GetKirchhoffMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetGetKirchhoffMatrix();</div> <p>Returns Kirchhoff matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p><strong>KirchhoffMatrix</strong> is another name for <strong>LaplacianMatrix</strong>.</p> </dd> <dt><strong><a name="getlaplacianmatrix" class="item"><strong>GetLaplacianMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetLaplacianMatrix();</div> <p>Returns Laplacian matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . deg(Vi) if i == j and deg(Vi) is the degree of vertex Vi <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj <br/> . 0 otherwise</div> </dd> <dt><strong><a name="getlargestcycle" class="item"><strong>GetLargestCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $CyclicPath = $Graph->GetLargestCycle();</div> <p>Returns a cyclic <em>Path</em> object corresponding to largest cycle in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getlargestedgecycle" class="item"><strong>GetLargestEdgeCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $CyclicPath = $Graph->GetLargestEdgeCycle($VertexID1, $VertexID2);</div> <p>Returns a cyclic <em>Path</em> object corresponding to largest cycle containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getlargestvertexcycle" class="item"><strong>GetLargestVertexCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $CyclicPath = $Graph->GetLargestVertexCycle($VertexID);</div> <p>Returns a cyclic <em>Path</em> object corresponding to largest cycle containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getleafvertices" class="item"><strong>GetLeafVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexIDs = $Graph->GetLeafVertices();</div> <p>Returns an array <em>VertexIDs</em> containing vertices with degree of 1 in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getmaximumdegree" class="item"><strong>GetMaximumDegree</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Degree = $Graph->GetMaximumDegree();</div> <p>Returns value of maximum vertex degree in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getmininumdegree" class="item"><strong>GetMininumDegree</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Degree = $Graph->GetMininumDegree();</div> <p>Returns value of minimum vertex degree in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getneighborhoodvertices" class="item"><strong>GetNeighborhoodVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexNeighborhoods = GetNeighborhoodVertices($StartVertexID);</div> <p>Returns an array <em>VertexNeighborhoods</em> containing references to arrays corresponding to neighborhood vertices around a specified <em>StartVertexID</em> at all possible radii levels.</p> </dd> <dt><strong><a name="getneighborhoodverticeswithradiusupto" class="item"><strong>GetNeighborhoodVerticesWithRadiusUpto</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexNeighborhoods = GetNeighborhoodVerticesWithRadiusUpto( $StartVertexID, $Radius);</div> <p>Returns an array <em>VertexNeighborhoods</em> containing references to arrays corresponding to neighborhood vertices around a specified <em>StartVertexID</em> upto specified <em>Radius</em> levels.</p> </dd> <dt><strong><a name="getneighborhoodverticeswithsuccessors" class="item"><strong>GetNeighborhoodVerticesWithSuccessors</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexNeighborhoods = GetNeighborhoodVerticesWithSuccessors( $StartVertexID);</div> <p>Returns vertex neighborhoods around a specified <em>StartVertexID</em>, along with their successor connected vertices, collected at all neighborhood radii as an array <em>VertexNeighborhoods</em> containing references to arrays with first value corresponding to vertex ID and second value as reference to an array containing its successor connected vertices.</p> <p>For a neighborhood vertex at each radius level, the successor connected vertices correspond to the neighborhood vertices at the next radius level. Consequently, the neighborhood vertices at the last radius level don't contain any successor vertices which fall outside the range of specified radius.</p> </dd> <dt><strong><a name="getneighborhoodverticeswithsuccessorsandradiusupto" class="item"><strong>GetNeighborhoodVerticesWithSuccessorsAndRadiusUpto</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexNeighborhoods = GetNeighborhoodVerticesWithSuccessors( $StartVertexID, $Radius);</div> <p>Returns vertex neighborhoods around a specified <em>StartVertexID</em>, along with their successor connected vertices, collected with in a specified <em>Radius</em> as an array <em>VertexNeighborhoods</em> containing references to arrays with first value corresponding to vertex ID and second value as reference to a list containing its successor connected vertices.</p> <p>For a neighborhood vertex at each radius level, the successor connected vertices correspond to the neighborhood vertices at the next radius level. Consequently, the neighborhood vertices at the last radius level don't contain any successor vertices which fall outside the range of specified radius.</p> </dd> <dt><strong><a name="getneighbors" class="item"><strong>GetNeighbors</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexIDs = $Graph->GetNeighbors($VertexID); <br/> $NumOfNeighbors = $Graph->GetNeighbors($VertexID);</div> <p>Returns an array <em>VertexIDs</em> containing vertices connected to <em>VertexID</em> of number of neighbors of a <em>VertextID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnormalizedlaplacianmatrix" class="item"><strong>GetNormalizedLaplacianMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetNormalizedLaplacianMatrix();</div> <p>Returns normalized Laplacian matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . 1 if i == j and deg(Vi) != 0 <br/> . -1/SQRT(deg(Vi) * deg(Vj)) if i != j and vertex Vi is adjacent to vertex Vj <br/> . 0 otherwise</div> </dd> <dt><strong><a name="getnumofcycles" class="item"><strong>GetNumOfCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfCycles();</div> <p>Returns number of cycles in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofcycleswithevensize" class="item"><strong>GetNumOfCyclesWithEvenSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfCyclesWithEvenSize();</div> <p>Returns number of cycles with even size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofcycleswithoddsize" class="item"><strong>GetNumOfCyclesWithOddSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfCyclesWithOddSize();</div> <p>Returns number of cycles with odd size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofcycleswithsize" class="item"><strong>GetNumOfCyclesWithSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfCyclesWithSize($CycleSize);</div> <p>Returns number of cycles with <em>CyclesSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofcycleswithsizegreaterthan" class="item"><strong>GetNumOfCyclesWithSizeGreaterThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfCyclesWithSizeGreaterThan( $CycleSize);</div> <p>Returns number of cycles with size greater than <em>CyclesSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofcycleswithsizelessthan" class="item"><strong>GetNumOfCyclesWithSizeLessThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfCyclesWithSizeLessThan($CycleSize);</div> <p>Returns number of cycles with size less than <em>CyclesSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofedgecycles" class="item"><strong>GetNumOfEdgeCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfEdgeCycles($VertexID1, $VertexID2);</div> <p>Returns number of cycles containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofedgecycleswithevensize" class="item"><strong>GetNumOfEdgeCyclesWithEvenSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfEdgeCyclesWithEvenSize($VertexID1, $VertexID2);</div> <p>Returns number of cycles containing edge between <em>VertexID1</em> and <em>VertexID2</em> with even size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofedgecycleswithoddsize" class="item"><strong>GetNumOfEdgeCyclesWithOddSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfEdgeCyclesWithOddSize($VertexID1, $VertexID2);</div> <p>Returns number of cycles containing edge between <em>VertexID1</em> and <em>VertexID2</em> with odd size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofedgecycleswithsize" class="item"><strong>GetNumOfEdgeCyclesWithSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfEdgeCyclesWithSize($VertexID1, $VertexID2, $CycleSize);</div> <p>Returns number of cycles containing edge between <em>VertexID1</em> and <em>VertexID2</em> with <em>CycleSize</em> size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofedgecycleswithsizegreaterthan" class="item"><strong>GetNumOfEdgeCyclesWithSizeGreaterThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfEdgeCyclesWithSizeGreaterThan( $VertexID1, $VertexID2, $CycleSize);</div> <p>Returns number of cycles containing edge between <em>VertexID1</em> and <em>VertexID2</em> with size greater than <em>CycleSize</em> size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofedgecycleswithsizelessthan" class="item"><strong>GetNumOfEdgeCyclesWithSizeLessThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfEdgeCyclesWithSizeLessThan( $VertexID1, $VertexID2, $CycleSize);</div> <p>Returns number of cycles containing edge between <em>VertexID1</em> and <em>VertexID2</em> with size less than <em>CycleSize</em> size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofvertexcycles" class="item"><strong>GetNumOfVertexCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfVertexCycles($VertexID);</div> <p>Returns number of cycles containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofvertexcycleswithevensize" class="item"><strong>GetNumOfVertexCyclesWithEvenSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfVertexCyclesWithEvenSize($VertexID);</div> <p>Returns number of cycles containing <em>VertexID</em> with even size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofvertexcycleswithoddsize" class="item"><strong>GetNumOfVertexCyclesWithOddSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfVertexCyclesWithOddSize($VertexID);</div> <p>Returns number of cycles containing <em>VertexID</em> with odd size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofvertexcycleswithsize" class="item"><strong>GetNumOfVertexCyclesWithSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfVertexCyclesWithSize($VertexID);</div> <p>Returns number of cycles containing <em>VertexID</em> with even size in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofvertexcycleswithsizegreaterthan" class="item"><strong>GetNumOfVertexCyclesWithSizeGreaterThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfVertexCyclesWithSizeGreaterThan( $VertexID, $CycleSize);</div> <p>Returns number of cycles containing <em>VertexID</em> with size greater than <em>CycleSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getnumofvertexcycleswithsizelessthan" class="item"><strong>GetNumOfVertexCyclesWithSizeLessThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> $NumOfCycles = $Graph->GetNumOfVertexCyclesWithSizeLessThan( $VertexID, $CycleSize);</div> <p>Returns number of cycles containing <em>VertexID</em> with size less than <em>CycleSize</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getpaths" class="item"><strong>GetPaths</strong></a></strong></dt> <dd> <div class="OptionsBox"> $PathsRefs = $Graph->GetPaths([$AllowCycles]);</div> <p>Returns a reference to an array of <em>Path</em> objects corresponding to paths of all possible lengths starting from each vertex with no sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getpathsbetween" class="item"><strong>GetPathsBetween</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->GetPathsBetween($StartVertexID, $EndVertexID);</div> <p>Returns an arrays of <em>Path</em> objects list of paths between <em>StartVertexID</em> and <em>EndVertexID</em>. For cyclic graphs, the list contains may contain more than one <em>Path</em> object.</p> </dd> <dt><strong><a name="getpathsstartingat" class="item"><strong>GetPathsStartingAt</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->GetPathsStartingAt($StartVertexID, [$AllowCycles]);</div> <p>Returns an array of <em>Path</em> objects corresponding to all possible lengths starting from a specified <em>StartVertexID</em> with no sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getpathsstartingatwithlength" class="item"><strong>GetPathsStartingAtWithLength</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->StartingAtWithLength($StartVertexID, $Length, $AllowCycles);</div> <p>Returns an array of <em>Path</em> objects corresponding to all paths starting from a specified <em>StartVertexID</em> with length <em>Length</em> and no sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getpathsstartingatwithlengthupto" class="item"><strong>GetPathsStartingAtWithLengthUpto</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->StartingAtWithLengthUpto($StartVertexID, $Length, $AllowCycles);</div> <p>Returns an array of <em>Path</em> objects corresponding to all paths starting from a specified <em>StartVertexID</em> with length upto <em>Length</em> and no sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getpathswithlength" class="item"><strong>GetPathsWithLength</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->GetPathsWithLength($Length, $AllowCycles);</div> <p>Returns an array of <em>Path</em> objects corresponding to to paths starting from each vertex in graph with specified <Length> and no sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getpathswithlengthupto" class="item"><strong>GetPathsWithLengthUpto</strong></a></strong></dt> <dd> <div class="OptionsBox"> @Paths = $Graph->GetPathsWithLengthUpto($Length, $AllowCycles);</div> <p>Returns an array of <em>Path</em> objects corresponding to to paths starting from each vertex in graph with length upto specified <em>Length</em> and no sharing of edges in paths traversed. By default, cycles are included in paths. A path containing a cycle is terminated at a vertex completing the cycle.</p> </dd> <dt><strong><a name="getsiedeladjacencymatrix" class="item"><strong>GetSiedelAdjacencyMatrix</strong></a></strong></dt> <dd> <div class="OptionsBox"> $GraphMatrix = $Graph->GetSiedelAdjacencyMatrix();</div> <p>Returns Siedel admittance matrix for <em>Graph</em> as a <em>GraphMatrix</em> object with row and column indices corresponding to graph vertices returned by GetVertices method.</p> <p>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:</p> <div class="OptionsBox"> . 0 if i == j <br/> . -1 if i != j and vertex Vi is adjacent to vertex Vj <br/> . 1 if i != j and vertex Vi is not adjacent to vertex Vj</div> </dd> <dt><strong><a name="getsizeoflargestcycle" class="item"><strong>GetSizeOfLargestCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Size = $Graph->GetSizeOfLargestCycle();</div> <p>Returns size of the largest cycle in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsizeoflargestedgecycle" class="item"><strong>GetSizeOfLargestEdgeCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Size = $Graph->GetSizeOfLargestEdgeCycle($VertexID1, $VertexID2);</div> <p>Returns size of the largest cycle containing egde between <em>VertextID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsizeoflargestvertexcycle" class="item"><strong>GetSizeOfLargestVertexCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Size = $Graph->GetSizeOfLargestVertexCycle($VertexID);</div> <p>Returns size of the largest cycle containing <em>VertextID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsizeofsmallestcycle" class="item"><strong>GetSizeOfSmallestCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Size = $Graph->GetSizeOfSmallestCycle();</div> <p>Returns size of the smallest cycle in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsizeofsmallestedgecycle" class="item"><strong>GetSizeOfSmallestEdgeCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Size = $Graph->GetSizeOfSmallestEdgeCycle($VertexID1, $VertexID2);</div> <p>Returns size of the smallest cycle containing egde between <em>VertextID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsizeofsmallestvertexcycle" class="item"><strong>GetSizeOfSmallestVertexCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Size = $Graph->GetSizeOfSmallestVertexCycle($VertexID);</div> <p>Returns size of the smallest cycle containing <em>VertextID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsmallestcycle" class="item"><strong>GetSmallestCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $CyclicPath = $Graph->GetSmallestCycle();</div> <p>Returns a cyclic <em>Path</em> object corresponding to smallest cycle in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsmallestedgecycle" class="item"><strong>GetSmallestEdgeCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $CyclicPath = $Graph->GetSmallestEdgeCycle($VertexID1, $VertexID2);</div> <p>Returns a cyclic <em>Path</em> object corresponding to smallest cycle containing edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getsmallestvertexcycle" class="item"><strong>GetSmallestVertexCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $CyclicPath = $Graph->GetSmallestVertexCycle($VertexID);</div> <p>Returns a cyclic <em>Path</em> object corresponding to smallest cycle containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="gettopologicallysortedvertices" class="item"><strong>GetTopologicallySortedVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexIDs = $Graph->GetTopologicallySortedVertices( [$RootVertexID]);</div> <p>Returns an array of <em>VertexIDs</em> sorted topologically starting from a specified <em>RootVertexID</em> or from an arbitrary vertex ID.</p> </dd> <dt><strong><a name="getvertex" class="item"><strong>GetVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $VertexValue = $Graph->GetVertex($VertexID);</div> <p>Returns vartex value for <em>VertexID</em> in a <em>Graph</em>. Vartex IDs and values are equivalent in the current implementation of <strong>Graph</strong>.</p> </dd> <dt><strong><a name="getvertexcycles" class="item"><strong>GetVertexCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetVertexCycles($VertexID);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to all cycles containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexcycleswithevensize" class="item"><strong>GetVertexCyclesWithEvenSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetVertexCyclesWithEvenSize($VertexID);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with even size containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexcycleswithoddsize" class="item"><strong>GetVertexCyclesWithOddSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetVertexCyclesWithOddSize($VertexID);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with odd size containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexcycleswithsize" class="item"><strong>GetVertexCyclesWithSize</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetVertexCyclesWithSize($VertexID, $CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size <em>CycleSize</em> containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexcycleswithsizegreaterthan" class="item"><strong>GetVertexCyclesWithSizeGreaterThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetVertexCyclesWithSizeGreaterThan($VertexID, $CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size greater than <em>CycleSize</em> containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexcycleswithsizelessthan" class="item"><strong>GetVertexCyclesWithSizeLessThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> @CyclicPaths = $Graph->GetVertexCyclesWithSizeLessThan($VertexID, $CycleSize);</div> <p>Returns an array <em>CyclicPaths</em> containing <em>Path</em> objects corresponding to cycles with size less than <em>CycleSize</em> containing <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexproperties" class="item"><strong>GetVertexProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> %VertexProperties = $Graph->GetVertexProperties($VertexID);</div> <p>Returns a hash <strong>VertexProperties</strong> containing all <strong>PropertyName</strong> and <strong>PropertyValue</strong> pairs associated with a <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexproperty" class="item"><strong>GetVertexProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Value = $Graph->GetVertexProperty($PropertyName, $VertexID);</div> <p>Returns value of <em>PropertyName</em> associated with a <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexwithlargestdegree" class="item"><strong>GetVertexWithLargestDegree</strong></a></strong></dt> <dd> <div class="OptionsBox"> $VertexID = $Graph->GetVertexWithLargestDegree();</div> <p>Returns <strong>VertexID</strong> with largest degree in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertexwithsmallestdegree" class="item"><strong>GetVertexWithSmallestDegree</strong></a></strong></dt> <dd> <div class="OptionsBox"> $VertexID = $Graph->GetVertexWithSmallestDegree();</div> <p>Returns <strong>VertexID</strong> with smallest degree in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getvertices" class="item"><strong>GetVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexIDs = $Graph->GetVertices(); <br/> $VertexCount = $Graph->GetVertices();</div> <p>Returns an array of <em>VertexIDs</em> corresponding to all vertices in a <em>Graph</em>; in a scalar context, number of vertices is returned.</p> </dd> <dt><strong><a name="getverticesproperty" class="item"><strong>GetVerticesProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> @PropertyValues = $Graph->GetVerticesProperty($PropertyName, @VertexIDs);</div> <p>Returns an array <em>PropertyValues</em> containing property values corresponding to <em>PropertyName</em> associated with with <em>VertexIDs</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="getverticeswithdegreelessthan" class="item"><strong>GetVerticesWithDegreeLessThan</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VertexIDs = $Graph->GetVerticesWithDegreeLessThan($Degree);</div> <p>Returns an array of <em>VertexIDs</em> containing vertices with degree less than <em>Degree</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hascycle" class="item"><strong>HasCycle</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasCycle(@VertexIDs);</div> <p>Returns 1 or 0 based on whether edges between successive pair of <em>VertexIDs</em> including an additional edge from the last to first vertex ID exists in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hasedge" class="item"><strong>HasEdge</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasEdge($VertexID1, $VertexID2);</div> <p>Returns 1 or 0 based on whether an edge between <em>VertexID1</em> and <em>VertexID2</em> exist in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hasedgeproperty" class="item"><strong>HasEdgeProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasEdgeProperty($PropertyName, $VertexID1, $VertexID2);</div> <p>Returns 1 or 0 based on whether <em>PropertyName</em> has already been associated with an edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hasedges" class="item"><strong>HasEdges</strong></a></strong></dt> <dd> <div class="OptionsBox"> @EdgesStatus = $Graph->HasEdges(@VertexIDs); <br/> $FoundEdgesCount = $Graph->HasEdges(@VertexIDs);</div> <p>Returns an array <em>EdgesStatus</em> containing 1s and 0s corresponding to whether edges between successive pairs of <em>VertexIDs</em> exist in a <em>Graph</em>. In a scalar context, number of edges found is returned.</p> </dd> <dt><strong><a name="hasfusedcycles" class="item"><strong>HasFusedCycles</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasFusedCycles();</div> <p>Returns 1 or 0 based on whether any fused cycles exist in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hasgraphproperty" class="item"><strong>HasGraphProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasGraphProperty($PropertyName);</div> <p>Returns 1 or 0 based on whether <em>PropertyName</em> has already been associated as a graph property as opposed to vertex or edge property in a <em>Graph</em>.</p> </dd> <dt><strong><a name="haspath" class="item"><strong>HasPath</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasPath(@VertexIDs));</div> <p>Returns 1 or 0 based on whether edges between all successive pairs of <em>VertexIDs</em> exist in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hasvertex" class="item"><strong>HasVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasVertex($VertexID);</div> <p>Returns 1 or 0 based on whether <em>VertexID</em> exists in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hasvertexproperty" class="item"><strong>HasVertexProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->HasGraphProperty($HasVertexProperty, $VertexID);</div> <p>Returns 1 or 0 based on whether <em>PropertyName</em> has already been associated with <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="hasvertices" class="item"><strong>HasVertices</strong></a></strong></dt> <dd> <div class="OptionsBox"> @VerticesStatus = $Graph->HasVertices(@VertexIDs); <br/> $VerticesFoundCount = $Graph->HasVertices(@VertexIDs);</div> <p>Returns an array <em></em> containing 1s and 0s corresponding to whether <em>VertexIDs</em> exist in a <em>Graph</em>. In a scalar context, number of vertices found is returned.</p> </dd> <dt><strong><a name="isacyclic" class="item"><strong>IsAcyclic</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsAcyclic();</div> <p>Returns 0 or 1 based on whether a cycle exist in a <em>Graph</em>.</p> </dd> <dt><strong><a name="isacyclicedge" class="item"><strong>IsAcyclicEdge</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsAcyclicEdge($VertexID1, $VertexID2);</div> <p>Returns 0 or 1 based on whether a cycle containing an edge between <em>VertexID1</em> and <em>VertexID2</em> exists in a <em>Graph</em>.</p> </dd> <dt><strong><a name="isacyclicvertex" class="item"><strong>IsAcyclicVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsAcyclicVertex($VertexID1);</div> <p>Returns 0 or 1 based on whether a cycle containing a <em>VertexID</em> exists in a <em>Graph</em>.</p> </dd> <dt><strong><a name="iscyclic" class="item"><strong>IsCyclic</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsCyclic();</div> <p>Returns 1 or 0 based on whether a cycle exist in a <em>Graph</em>.</p> </dd> <dt><strong><a name="iscyclicedge" class="item"><strong>IsCyclicEdge</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsCyclicEdge($VertexID1, $VertexID2);</div> <p>Returns 1 or 0 based on whether a cycle containing an edge between <em>VertexID1</em> and <em>VertexID2</em> exists in a <em>Graph</em>.</p> </dd> <dt><strong><a name="iscyclicvertex" class="item"><strong>IsCyclicVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsCyclicVertex($VertexID1);</div> <p>Returns 1 or 0 based on whether a cycle containing a <em>VertexID</em> exists in a <em>Graph</em>.</p> </dd> <dt><strong><a name="isgraph" class="item"><strong>IsGraph</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = Graph::IsGraph($Object);</div> <p>Returns 1 or 0 based on whether <em>Object</em> is a <strong>Graph</strong> object.</p> </dd> <dt><strong><a name="isisolatedvertex" class="item"><strong>IsIsolatedVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsIsolatedVertex($VertexID);</div> <p>Returns 1 or 0 based on whether <em>VertexID</em> is an isolated vertex in a <em>Graph</em>. A vertex with zero as its degree value is considered an isolated vertex.</p> </dd> <dt><strong><a name="isleafvertex" class="item"><strong>IsLeafVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsLeafVertex($VertexID);</div> <p>Returns 1 or 0 based on whether <em>VertexID</em> is an isolated vertex in a <em>Graph</em>. A vertex with one as its degree value is considered an isolated vertex.</p> </dd> <dt><strong><a name="isunicyclic" class="item"><strong>IsUnicyclic</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsUnicyclic();</div> <p>Returns 1 or 0 based on whether only one cycle is present in a <em>Graph</em>.</p> </dd> <dt><strong><a name="isunicyclicedge" class="item"><strong>IsUnicyclicEdge</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsUnicyclicEdge($VertexID1, $VertexID2);</div> <p>Returns 1 or 0 based on whether only one cycle contains the edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="isunicyclicvertex" class="item"><strong>IsUnicyclicVertex</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Status = $Graph->IsUnicyclicVertex($VertexID);</div> <p>Returns 1 or 0 based on whether only one cycle contains <em>VertexID</em> in a <em>Graph</em>.</p> </dd> <dt><strong><a name="setactivecyclicpaths" class="item"><strong>SetActiveCyclicPaths</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetActiveCyclicPaths($CyclicPathsType);</div> <p>Sets the type of cyclic paths to use during all methods related to cycles and returns <em>Graph</em>. Possible values for cyclic paths: <em>Independent or All</em>.</p> </dd> <dt><strong><a name="setedgeproperties" class="item"><strong>SetEdgeProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetEdgeProperties($VertexID1, $VertexID2, @NamesAndValues);</div> <p>Associates property names and values corresponding to successive pairs of values in <em>NamesAndValues</em> to an edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="setedgeproperty" class="item"><strong>SetEdgeProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetEdgeProperty($Name, $Value, $VertexID1, $VertexID2);</div> <p>Associates property <em>Name</em> and <em>Value</em> to an edge between <em>VertexID1</em> and <em>VertexID2</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="setedgesproperty" class="item"><strong>SetEdgesProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetEdgesProperty($Name, @ValuesAndVertexIDs);</div> <p>Associates a same property <em>Name</em> but different <em>Values</em> for different edges specified using triplets of <em>PropertyValue, $VertexID1, $VertexID2</em> via <em>ValuesAndVertexIDs</em> in a <em>graph</em>.</p> </dd> <dt><strong><a name="setgraphproperties" class="item"><strong>SetGraphProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetGraphProperties(%NamesAndValues);</div> <p>Associates property names and values <em>NamesAndValues</em> hash to graph as opposed to vertex or edge and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="setgraphproperty" class="item"><strong>SetGraphProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetGraphProperty($Name, $Value);</div> <p>Associates property <em>Name</em> and <em>Value</em> to graph as opposed to vertex or edge and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="setvertexproperties" class="item"><strong>SetVertexProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetVertexProperties($VertexID, @NamesAndValues);</div> <p>Associates property names and values corresponding to successive pairs of values in <em>NamesAndValues</em> to <em>VertexID</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="setvertexproperty" class="item"><strong>SetVertexProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetVertexProperty($Name, $Value, $VertexID);</div> <p>Associates property <em>Name</em> and <em>Value</em> to <em>VertexID</em> in a <em>Graph</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="setverticesproperty" class="item"><strong>SetVerticesProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->SetVerticesProperty($Name, @ValuesAndVertexIDs));</div> <p>Associates a same property <em>Name</em> but different <em>Values</em> for different vertices specified using doublets of <em>PropertyValue, $VertexID</em> via <em>ValuesAndVertexIDs</em> in a <em>graph</em>.</p> </dd> <dt><strong><a name="stringifyedgesproperties" class="item"><strong>StringifyEdgesProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $String = $Graph->StringifyEdgesProperties();</div> <p>Returns a string containing information about properties associated with all edges in a <em>Graph</em> object.</p> </dd> <dt><strong><a name="stringifygraph" class="item"><strong>StringifyGraph</strong></a></strong></dt> <dd> <div class="OptionsBox"> $String = $Graph->StringifyGraph();</div> <p>Returns a string containing information about <em>Graph</em> object.</p> </dd> <dt><strong><a name="stringifygraphproperties" class="item"><strong>StringifyGraphProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $String = $Graph->StringifyGraphProperties();</div> <p>Returns a string containing information about properties associated with graph as opposed to vertex. or an edge in a <em>Graph</em> object</p> </dd> <dt><strong><a name="stringifyproperties" class="item"><strong>StringifyProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $String = $Graph->StringifyProperties();</div> <p>Returns a string containing information about properties associated with graph, vertices, and edges in a <em>Graph</em> object.</p> </dd> <dt><strong><a name="stringifyverticesandedges" class="item"><strong>StringifyVerticesAndEdges</strong></a></strong></dt> <dd> <div class="OptionsBox"> $String = $Graph->StringifyVerticesAndEdges();</div> <p>Returns a string containing information about vertices and edges in a <em>Graph</em> object.</p> </dd> <dt><strong><a name="stringifyverticesproperties" class="item"><strong>StringifyVerticesProperties</strong></a></strong></dt> <dd> <div class="OptionsBox"> $String = $Graph->StringifyVerticesProperties();</div> <p>Returns a string containing information about properties associated with vertices a <em>Graph</em> object.</p> </dd> <dt><strong><a name="updateedgeproperty" class="item"><strong>UpdateEdgeProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->UpdateEdgeProperty($Name, $Value, $VertexID1, $VertexID2);</div> <p>Updates property <em>Value</em> for <em>Name</em> associated with an edge between <em>VertexID1</em> and <em>VertexID1</em> and returns <em>Graph</em>.</p> </dd> <dt><strong><a name="updatevertexproperty" class="item"><strong>UpdateVertexProperty</strong></a></strong></dt> <dd> <div class="OptionsBox"> $Graph->UpdateVertexProperty($Name, $Value, $VertexID);</div> <p>Updates property <em>Value</em> for <em>Name</em> associated with <em>VertexID</em> and returns <em>Graph</em>.</p> </dd> </dl> <p> </p> <h2>AUTHOR</h2> <p><a href="mailto:msud@san.rr.com">Manish Sud</a></p> <p> </p> <h2>SEE ALSO</h2> <p><a href="./CyclesDetection.html">CyclesDetection.pm</a>, <a href="./Path.html">Path.pm</a>, <a href="./PathGraph.html">PathGraph.pm</a>, <a href="./PathsTraversal.html">PathsTraversal.pm</a> </p> <p> </p> <h2>COPYRIGHT</h2> <p>Copyright (C) 2015 Manish Sud. All rights reserved.</p> <p>This file is part of MayaChemTools.</p> <p>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.</p> <p> </p><p> </p><div class="DocNav"> <table width="100%" border=0 cellpadding=0 cellspacing=2> <tr align="left" valign="top"><td width="33%" align="left"><a href="./PathsTraversal.html" title="PathsTraversal.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./HTMLUtil.html" title="HTMLUtil.html">Next</a></td><td width="34%" align="middle"><strong>March 29, 2015</strong></td><td width="33%" align="right"><strong>Graph.pm</strong></td></tr> </table> </div> <br /> <center> <img src="../../images/h2o2.png"> </center> </body> </html>