Y~      !"#$%&'()*+,-./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 graph&Retrieve the edges of a graph as pairs$Tell if a vertex exists in the graph*Retrieve the adjacent vertices of a vertex*Total number of incident edges of a vertex(Degrees of a all the vertices in a graphMaximum degree of a graphMinimum degree of a graphbInsert a vertex into a graph | If the graph already contains the vertex leave the graph untoucheduInsert a many vertices into a graph | New vertices are inserted and already contained vertices are left | untouched(Tell if a graph is simple | A graph is simple& if it has no multiple edges nor loops )Tell if a graph is regular | A graph is regularF when all of its vertices have the same | number of adjacent vertices!CGenerate a graph of Int vertices from an adjacency | square matrix"1Get the adjacency matrix representation of a grah#Construct an undirected   between two vertices$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 same,To  Ns are equal if they point to the same vertices, regardless of the | direction7  !"#$%&'()*+,-./0123456+  !"#$%&'()*7  !"  #$6543210/.-,+%&'()*    !"#$%&'()*+,-./0123456Safe9;T=<The Degree Sequence of a simple 'UGraph is a list of degrees@!Probability value between 0 and 1B Undirected Graph of Vertices in v and Edges with attributes in eE Construct a @ valueF:Generate a random 'UGraph of the ErdQs Rnyi G(n, p) modelHO(n)4 Remove a vertex from a 'UGraph if present | Every  ( incident to this vertex is also removedIO(log n) Insert an undirected   into a 'UGraph | The involved vertices are inserted if don't exist. If the graph already | contains the Edge, its attribute is updatedJ O(m*log n) Insert many directed  "s into a 'UGraph | Same rules as I are appliedKO(log n) Remove the undirected  F from a 'UGraph if present | The involved vertices are left untouchedLSame as K" but the edge is an unordered pairMO(log n) Remove the undirected  D from a 'UGraph if present | The involved vertices are also removedNSame as M" but the edge is an unordered pairOO(n*m) Retrieve the  s of a 'UGraphPO(log n) Tell if an undirected   exists in the graphQSame as P" but the edge is an unordered pairRRetrieve the incident   s of a VertexS"Tell if two 'UGraph are isomorphicU Construct a =? from a list of degrees | Negative degree values are discardedVGet the =, of a simple 'UGraph | If the graph is not simple (see ) the result is NothingW Tell if a =3 is a Graphical Sequence | A Degree Sequence is a Graphical Sequence, if a corresponding 'UGraph for | it existsX#Get the corresponding 'UGraph of a = | If the = is not graphical (see W) the | result is Nothing=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ=>?@ABCDEFGHIJKLMNOPQRSTUVWXBCDZY@AEFGHIJKLMNOPQRST=>?UVWX=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZNonec.Plot an undirected 'UGraph to a PNG image filedSame as c# but open the resulting image with xdg-opencdcdcdcdSafeTeThe Degree Sequence of a f) is a list of pairs (Indegree, Outdegree)fDirected Graph of Vertices in v and Arcs with attributes in eiO(n) Remove a vertex from a f if present | Every ( incident to this vertex is also removedjO(log n) Insert a directed  into a fy | The involved vertices are inserted if don't exist. If the graph already | contains the Arc, its attribute is updatedk O(m*log n) Insert many directed  s into a f | Same rules as j are appliedlO(log n) Remove the directed  from a f7 if present | The involved vertices are left untouchedmSame as l but the arc is an ordered pairnO(log n) Remove the directed  from a f5 if present | The involved vertices are also removedoSame as n but the arc is an ordered pairpO(n*m) Retrieve the s of a fqSame as pF but the arcs are ordered pairs, and their attributes are | discardedrO(log n) Tell if a directed  exists in the graphsSame as r but the arc is an ordered pairtRetrieve the inbounding  s of a VertexuRetrieve the outbounding  s of a VertexvRetrieve the incident 5s of a Vertex | Both inbounding and outbounding arcsw Tell if a f is symmetric | All of its s are bidirectedx Tell if a f* is oriented | There are none bidirected s | Note: This is not the opposite of wy Tell if a f is isolated | A graph is isolatedR if it has no edges, that is, it has a degree of 0 | TODO: What if it has a loop?z1Indegree 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 f}#Outdegree of all the vertices in a f~ Tell if a f$ is balanced | A Directed Graph is balanced when its indegree = outdegree Tell if a f# 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 sink Tell if a e is a Directed Graphic | A Directed Graphic! is a Degree Sequence for wich a fG exists TODO: Kleitman Wang | Fulkerson Chen Anstee theorem algorithms!efghijklmnopqrstuvwxyz{|}~efghijklmnopqrstuvwxyz{|}~!fgheijklmnopqrstuvwxyz{|}~efghijklmnopqrstuvwxyz{|}~Safe9Tell if a 'UGraph is connected | An Undirected Graph is  connected7 when there is a path between every pair | of vertices<Tell if a 'UGraph is disconnected | An Undirected Graph is  disconnected when its not  connected . See | B TODO: An edgeles graph with two or more vertices is disconnectedDTell if two vertices of a 'UGraph are connected | Two vertices are  connected! if it exists a path between themGTell if two vertices of a 'UGraph are disconnected | Two vertices are  disconnected( if it doesn't exist a path between them:Retrieve all the unreachable vertices of a 'UGraph | The unreachable vertices are those with no adjacent Edges Tell if a f, is weakly connected | A Directed Graph is weakly connected* if the equivalent undirected graph | is  connected      !"#$%&'()*+,-./0123456789:;<=>?@AABCDEEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefAgghJijklmnopqrstuvwxyz{|}$~'graphite-0.2.0.0-8cdgbhtKQUlLBKjPXGoEUCData.Graph.TypesData.Graph.UGraphData.Graph.VisualizeData.Graph.DGraphData.Graph.ConnectivityLinksLabeledlabelWeightedweightIsEdgetoPairisLoopArcEdgeGraphemptyordersizevertices edgePairscontainsVertexadjacentVertices vertexDegreedegrees maxDegree minDegree insertVertexinsertVerticescontainsEdgePairincidentEdgePairsinsertEdgePairremoveEdgePairremoveEdgePairAndVerticesisSimple isRegularfromAdjacencyMatrixtoAdjacencyMatrix<->--> arbitraryEdge insertLinkgetLinks linksToArcs linksToEdges hashMapInsert$fEqArc$fEqEdge$fArbitraryArc$fArbitraryEdge $fLabeled(,) $fWeighted(,) $fLabeled[]$fWeightedDouble$fWeightedFloat $fWeightedInt $fIsEdgeArc $fIsEdgeEdge $fShowEdge $fReadEdge $fOrdEdge $fShowArc $fReadArc$fOrdArcDegreeSequenceunDegreeSequence ProbabilityPUGraphunUGraph probability erdosRenyiIO randomMatIO removeVertex insertEdge insertEdges removeEdge removeEdge'removeEdgeAndVerticesremoveEdgeAndVertices'edges containsEdge containsEdge' incidentEdges areIsomorphic isomorphismdegreeSequencegetDegreeSequenceisGraphicalSequencefromGraphicalSequence$fArbitraryUGraph $fGraphUGraph $fEqUGraph $fShowUGraph$fEqProbability$fOrdProbability$fShowProbability$fEqDegreeSequence$fOrdDegreeSequence$fShowDegreeSequenceplotIO plotXdgIODGraphunDGraph insertArc insertArcs removeArc removeArc'removeArcAndVerticesremoveArcAndVertices'arcsarcs' containsArc containsArc'inboundingArcsoutboundingArcs incidentArcs isSymmetric isOriented isIsolatedvertexIndegreevertexOutdegree indegrees outdegrees isBalancedisSourceisSink isInternalisDirectedGraphic$fArbitraryDGraph $fGraphDGraph $fEqDGraph $fShowDGraph isConnectedisDisconnected areConnectedareDisconnectedunreachableVerticesisWeaklyConnected labeledNodes labeledEdgestoDot'