̔      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Safe9;T+Each vertex maps to a ' value so it can poit to other vertices4Labeled Edge attributes | Useful for graph plottingJWeighted Edge attributes | Useful for computing some algorithms on graphs2Convert an edge to a pair discargind its attribute-Tell if an edge is a loop | An edge forms a loop- if both of its ends point to the same vertex$Directed Arc with attribute of type e between to Vertices of type v 'Undirected Edge with attribute of type e between to Vertices of type v :The Empty (order-zero) graph with no vertices and no edges%Retrieve the order of a graph | The order% of a graph is its number of vertices$Retrieve the size of a graph | The size" of a graph is its number of edges Retrieve the vertices of a graphRetrieve the edges of a graph$Tell if a vertex exists in the graph!Tell if two vertices are adjacent*Retrieve the adjacent vertices of a vertex^Retrieve the vertices that are directly reachable from a particular | vertex. | A vertex is directly reachable/ to other if there is an edge that | connects from one vertex to< the other | Every vertex is directly reachable from itself*Total number of incident edges of a vertex(Degrees of a all the vertices in a graphMaximum degree of a graphMinimum degree of a graphAverage degree of a graphnDensity of a graph | The ratio of the number of existing edges in the graph to the number of | posible edgesbInsert a vertex into a graph | If the graph already contains the vertex leave the graph untoucheduInsert a many vertices into a graph | New vertices are inserted and already contained vertices are left | untouched#Tell if an edge exists in the graph'Retrieve the incident edges of a vertex Insert an edge into a graph | The involved vertices are inserted if don't exist. If the graph already | contains the edge, its attribute is updated!PRemove the edge from a graph present | The involved vertices are left untouched"QRemove the edge from a graph if present | The involved vertices are also removed#(Tell if a graph is simple | A graph is simple& if it has no multiple edges nor loops$)Tell if a graph is regular | A graph is regularF when all of its vertices have the same | number of adjacent vertices%CGenerate a graph of Int vertices from an adjacency | square matrix&1Get the adjacency matrix representation of a grah'Construct an undirected   between two vertices(Construct a directed  between two vertices)Edges generator*pInsert a link directed to *v* with attribute *a* | If the connnection already exists, the attribute is replaced+ Get the links for a given vertex,Get 6s from an association list of vertices and their links-Get  6s from an association list of vertices and their links.O(log n) Associate the specified value with the specified key in this map. | If this map previously contained a mapping for the key, leave the map | intact./To Qs are equal if they point to the same vertices, and the directions | is the same0To  Ns are equal if they point to the same vertices, regardless of the | direction;  !"#$%&'()*+,-./0123456789:/ # !"$%&'()*+,-.;  !"#$%&  '(:9876543210/)*+,-.    !"#$%&'()*+,-./0123456789:Safe9;TA The Degree Sequence of a simple D is a list of degreesD Undirected Graph of Vertices in v and Edges with attributes in eGO(n) Remove a vertex from a D if present | Every  ( incident to this vertex is also removedHO(log n) Insert an undirected   into a Dz | The involved vertices are inserted if don't exist. If the graph already | contains the Edge, its attribute is updatedI O(m*log n) Insert many directed   s into a D | Same rules as H are appliedJO(log n) Remove the undirected   from a D7 if present | The involved vertices are left untouchedKSame as J" but the edge is an unordered pairLO(log n) Remove the undirected   from a D5 if present | The involved vertices are also removedMSame as L" but the edge is an unordered pairNO(n*m) Retrieve the  s of a DOO(log n) Tell if an undirected   exists in the graphPSame as O" but the edge is an unordered pairQRetrieve the incident   s of a VertexR Tell if two D are isomorphicT Construct a A? from a list of degrees | Negative degree values are discardedUGet the A of a simple D | If the graph is not simple (see #) the result is NothingV Tell if a A3 is a Graphical Sequence | A Degree Sequence is a Graphical Sequence if a corresponding D for | it existsWGet the corresponding D of a A | If the A is not graphical (see V) the | result is NothingABCDEFGHIJKLMNOPQRSTUVWXYABCDEFGHIJKLMNOPQRSTUVWDEFYXGHIJKLMNOPQRSABCTUVWABCDEFGHIJKLMNOPQRSTUVWXYSafeT_!Probability value between 0 and 1a Construct a _ valueb1Generate a random ErdQs Rnyi G(n, p) model graphc>Generate a random square binary matrix | Useful for use with %_`abc_`abc_`abc_`abcSafeTgThe Degree Sequence of a h) is a list of pairs (Indegree, Outdegree)hDirected Graph of Vertices in v and Arcs with attributes in ekO(n) Remove a vertex from a h if present | Every ( incident to this vertex is also removedlO(log n) Insert a directed  into a hy | The involved vertices are inserted if don't exist. If the graph already | contains the Arc, its attribute is updatedm O(m*log n) Insert many directed  s into a h | Same rules as l are appliednO(log n) Remove the directed  from a h7 if present | The involved vertices are left untouchedoSame as n but the arc is an ordered pairpO(log n) Remove the directed  from a h5 if present | The involved vertices are also removedqSame as p but the arc is an ordered pairrO(n*m) Retrieve the s of a hsSame as rF but the arcs are ordered pairs, and their attributes are | discardedtO(log n) Tell if a directed  exists in the graphuSame as t but the arc is an ordered pairvRetrieve the inbounding  s of a VertexwRetrieve the outbounding  s of a VertexxRetrieve the incident 5s of a Vertex | Both inbounding and outbounding arcsy Tell if a h is symmetric | All of its s are bidirectedz Tell if a h* is oriented | There are none bidirected s | Note: This is not the opposite of y{1Indegree of a vertex | The number of inbounding  s to a vertex|3Outdegree of a vertex | The number of outbounding s from a vertex}#Indegrees of all the vertices in a h~#Outdegree of all the vertices in a h Tell if a h$ is balanced | A Directed Graph is balanced when its indegree = outdegree Tell if a h# is regular | A Directed Graph is regularT when all of its vertices have the same number | of adjacent vertices AND when the indegree and  outdegree+ of each vertex | are equal to each toher..Tell if a vertex is a source | A vertex is a source when its  indegree = 0,Tell if a vertex is a sink | A vertex is a sink when its  outdegree = 0.Tell if a vertex is internal | A vertex is a internal when its neither a source nor a sinkConvert a directed h to an undirected UGraph by converting all of | its s into  s Tell if a g is a Directed Graphic | A Directed Graphic! is a Degree Sequence for wich a hG exists TODO: Kleitman Wang | Fulkerson Chen Anstee theorem algorithms!ghijklmnopqrstuvwxyz{|}~ghijklmnopqrstuvwxyz{|}~!hijgklmnopqrstuvwxyz{|}~ghijklmnopqrstuvwxyz{|}~NonePlot an undirected D to a PNG image fileSame as # but open the resulting image with xdg-openPlot a directed h to a PNG image fileSame as # but open the resulting image with xdg-open  SafeTBTell if two vertices of a graph are connected | Two vertices are  connectede if it exists a path between them | The order of the vertices is relevant when the graph is directedTell if two vertices of a D& are disconnected | Two vertices are  disconnected( if it doesn't exist a path between them,Tell if a vertex is isolated | A vertex is isolated@ if it has no incidet edges, that is, it has a degree | of zero7Tell if a graph is connected | An Undirected Graph is  connected7 when there is a path between every pair | of vertices Tell if a h, is weakly connected | A Directed Graph is weakly connected* if the underlying undirected graph | is  connected Tell if a h. is strongly connected | A Directed Graph is strongly connected< if it contains a directed path | on every pair of vertices      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFFGHHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghiFjjkJlmnopqrstuvwxyz{|}~)'graphite-0.3.0.0-CC0fsgAE4GP3PKo0ITqZ7yData.Graph.TypesData.Graph.UGraphData.Graph.GenerationData.Graph.DGraphData.Graph.VisualizeData.Graph.ConnectivityLinksLabeledlabelWeightedweightIsEdgetoPairisLoopArcEdgeGraphemptyordersizevertices edgePairscontainsVertex areAdjacentadjacentVerticesdirectlyReachableVertices vertexDegreedegrees maxDegree minDegree avgDegreedensity insertVertexinsertVerticescontainsEdgePairincidentEdgePairsinsertEdgePairremoveEdgePairremoveEdgePairAndVerticesisSimple isRegularfromAdjacencyMatrixtoAdjacencyMatrix<->--> arbitraryEdge insertLinkgetLinks linksToArcs linksToEdges hashMapInsert$fEqArc$fEqEdge$fArbitraryArc$fArbitraryEdge $fLabeled(,) $fWeighted(,) $fLabeled[]$fWeightedDouble$fWeightedFloat $fWeightedInt $fIsEdgeArc $fIsEdgeEdge $fShowEdge $fReadEdge $fOrdEdge $fShowArc $fReadArc$fOrdArcDegreeSequenceunDegreeSequenceUGraphunUGraph removeVertex insertEdge insertEdges removeEdge removeEdge'removeEdgeAndVerticesremoveEdgeAndVertices'edges containsEdge containsEdge' incidentEdges areIsomorphic isomorphismdegreeSequencegetDegreeSequenceisGraphicalSequencefromGraphicalSequence $fGraphUGraph$fArbitraryUGraph $fEqUGraph $fShowUGraph$fEqDegreeSequence$fOrdDegreeSequence$fShowDegreeSequence ProbabilityP probability erdosRenyiIO randomMatIO$fEqProbability$fOrdProbability$fShowProbabilityDGraphunDGraph insertArc insertArcs removeArc removeArc'removeArcAndVerticesremoveArcAndVertices'arcsarcs' containsArc containsArc'inboundingArcsoutboundingArcs incidentArcs isSymmetric isOrientedvertexIndegreevertexOutdegree indegrees outdegrees isBalancedisSourceisSink isInternal toUndirectedisDirectedGraphic$fArbitraryDGraph $fGraphDGraph $fEqDGraph $fShowDGraphplotUndirectedIOplotUndirectedXdgIOplotDirectedIOplotDirectedXdgIO areConnectedareDisconnected isIsolated isConnectedisWeaklyConnectedisStronglyConnected labeledNodes labeledEdges labeledArcstoUndirectedDot toDirectedDot