When an edge in the MATCH clause is not given an alias, this edge can still be referenced by the edge column name. During translation, an edge without an explicit alias will be assigned a default alias, and as a result, the edge column name must be replaced by the assigned alias.
Inheritance: WSqlFragmentVisitor
        /// <summary>
        /// Constructs the graph pattern specified by the MATCH clause. 
        /// The graph pattern may consist of multiple fully-connected sub-graphs.
        /// </summary>
        /// <param name="query">The SELECT query block</param>
        /// <returns>A graph object contains all the connected componeents</returns>
        private MatchGraph ConstructGraph(WSelectQueryBlock query)
        {
            if (query == null || query.MatchClause == null)
                return null;

            var columnsOfNodeTables = _graphMetaData.ColumnsOfNodeTables;
            var nodeViewMapping = _graphMetaData.NodeViewMapping;
            var unionFind = new UnionFind();
            var edgeColumnToAliasesDict = new Dictionary<string, List<string>>(StringComparer.OrdinalIgnoreCase);
            var pathDictionary = new Dictionary<string, MatchPath>(StringComparer.OrdinalIgnoreCase);
            var reversedEdgeDict = new Dictionary<string, MatchEdge>();
            var matchClause = query.MatchClause;
            var nodes = new Dictionary<string, MatchNode>(StringComparer.OrdinalIgnoreCase);
            var connectedSubGraphs = new List<ConnectedComponent>();
            var subGrpahMap = new Dictionary<string, ConnectedComponent>(StringComparer.OrdinalIgnoreCase);
            var parent = new Dictionary<string, string>(StringComparer.OrdinalIgnoreCase);
            unionFind.Parent = parent;

            // Constructs the graph pattern specified by the path expressions in the MATCH clause
            foreach (var path in matchClause.Paths)
            {
                var index = 0;
                MatchEdge preEdge = null;
                for (var count = path.PathEdgeList.Count; index < count; ++index)
                {
                    var currentNodeTableRef = path.PathEdgeList[index].Item1;
                    var currentEdgeColumnRef = path.PathEdgeList[index].Item2;
                    var currentNodeExposedName = currentNodeTableRef.BaseIdentifier.Value;
                    var nextNodeTableRef = index != count - 1
                        ? path.PathEdgeList[index + 1].Item1
                        : path.Tail;
                    var nextNodeExposedName = nextNodeTableRef.BaseIdentifier.Value;
                    var patternNode = nodes.GetOrCreate(currentNodeExposedName);
                    if (patternNode.NodeAlias == null)
                    {
                        patternNode.NodeAlias = currentNodeExposedName;
                        patternNode.Neighbors = new List<MatchEdge>();
                        patternNode.External = false;
                        var nodeTable = _context[currentNodeExposedName] as WNamedTableReference;
                        if (nodeTable != null)
                        {
                            patternNode.NodeTableObjectName = nodeTable.TableObjectName;
                            if (patternNode.NodeTableObjectName.SchemaIdentifier == null)
                                patternNode.NodeTableObjectName.Identifiers.Insert(0, new Identifier {Value = "dbo"});
                        }
                    }

                    Identifier edgeIdentifier = currentEdgeColumnRef.MultiPartIdentifier.Identifiers.Last();
                    string schema = patternNode.NodeTableObjectName.SchemaIdentifier.Value.ToLower();
                    string nodeTableName = patternNode.NodeTableObjectName.BaseIdentifier.Value;
                    string bindTableName =
                        _context.EdgeNodeBinding[
                            new Tuple<string, string>(nodeTableName.ToLower(), edgeIdentifier.Value.ToLower())].ToLower();
                    var bindNodeTableObjName = new WSchemaObjectName(
                        new Identifier {Value = schema},
                        new Identifier {Value = bindTableName}
                        );
                    var edgeColumn =
                        columnsOfNodeTables[
                            WNamedTableReference.SchemaNameToTuple(bindNodeTableObjName)][
                                currentEdgeColumnRef.MultiPartIdentifier.Identifiers.Last().Value];
                    string edgeAlias = currentEdgeColumnRef.Alias;
                    //string revEdgeAlias = edgeAlias;
                    bool isReversed = path.IsReversed || edgeColumn.EdgeInfo.IsReversedEdge;
                    string currentRevEdgeName = null;

                    // get original edge name
                    var currentEdgeName = currentEdgeColumnRef.MultiPartIdentifier.Identifiers.Last().Value;
                    var originalSourceName = isReversed ?
                        (_context[nextNodeExposedName] as WNamedTableReference).TableObjectName.BaseIdentifier.Value
                        : (_context[currentNodeExposedName] as WNamedTableReference).TableObjectName.BaseIdentifier.Value;

                    if (isReversed)
                    {
                        var i = currentEdgeName.IndexOf(originalSourceName, StringComparison.OrdinalIgnoreCase) +
                            originalSourceName.Length;
                        currentRevEdgeName = currentEdgeName.Substring(i + 1,
                            currentEdgeName.Length - "Reversed".Length - i - 1);
                    }
                    else
                    {
                        var srcTuple = WNamedTableReference.SchemaNameToTuple(patternNode.NodeTableObjectName);
                        // [nodeView]-[edge]->[node/nodeView]
                        if (edgeColumn.Role == WNodeTableColumnRole.Edge && nodeViewMapping.ContainsKey(srcTuple))
                        {
                            var physicalNodeName =
                                _context.EdgeNodeBinding[new Tuple<string, string>(srcTuple.Item2, currentEdgeName.ToLower())];
                            currentRevEdgeName = physicalNodeName + "_" + currentEdgeName + "Reversed";
                        }
                        else
                        {
                            currentRevEdgeName = originalSourceName + "_" + currentEdgeName + "Reversed";
                        }
                    }

                    if (edgeAlias == null)
                    {
                        edgeAlias = !isReversed
                            ? string.Format("{0}_{1}_{2}", currentNodeExposedName, currentEdgeName, nextNodeExposedName)
                            : string.Format("{0}_{1}_{2}", nextNodeExposedName, currentRevEdgeName, currentNodeExposedName);

                        //when the current edge is a reversed edge, the key should still be the original edge name
                        //e.g.: TestDeleteEdgeWithTableAlias
                        var edgeNameKey = isReversed ? currentRevEdgeName : currentEdgeName;
                        if (edgeColumnToAliasesDict.ContainsKey(edgeNameKey))
                        {
                            edgeColumnToAliasesDict[edgeNameKey].Add(edgeAlias);
                        }
                        else
                        {
                            edgeColumnToAliasesDict.Add(edgeNameKey, new List<string> { edgeAlias });
                        }
                    }

                    MatchEdge edge, revEdge;
                    if (currentEdgeColumnRef.MinLength == 1 && currentEdgeColumnRef.MaxLength == 1)
                    {
                        var isEdgeView = edgeColumn.Role == WNodeTableColumnRole.EdgeView;
                        var hasRevEdge = edgeColumn.EdgeInfo.HasReversedEdge;
                        edge = new MatchEdge
                        {
                            IsEdgeView = isEdgeView,
                            IsReversedEdge = false,
                            HasReversedEdge = hasRevEdge,
                            SourceNode = patternNode,
                            EdgeColumn = currentEdgeColumnRef,
                            EdgeAlias = edgeAlias,
                            BindNodeTableObjName = bindNodeTableObjName,
                        };
                        _context.AddEdgeReference(edge);

                        if (hasRevEdge)
                        {
                            revEdge = new MatchEdge
                            {
                                IsEdgeView = isEdgeView,
                                IsReversedEdge = true,
                                SinkNode = patternNode,
                                EdgeColumn = new WEdgeColumnReferenceExpression()
                                {
                                    ColumnType = currentEdgeColumnRef.ColumnType,
                                    Alias = currentEdgeColumnRef.Alias,
                                    MaxLength = currentEdgeColumnRef.MaxLength,
                                    MinLength = currentEdgeColumnRef.MinLength,
                                    AttributeValueDict = currentEdgeColumnRef.AttributeValueDict,
                                    MultiPartIdentifier = new WMultiPartIdentifier(new Identifier()
                                    {
                                        QuoteType = currentEdgeColumnRef.MultiPartIdentifier.Identifiers.Last().QuoteType,
                                        Value = currentRevEdgeName,
                                    }),
                                },
                                EdgeAlias = edgeAlias,
                                //EdgeAlias = revEdgeAlias,
                            };
                            reversedEdgeDict[edge.EdgeAlias] = revEdge;
                        }
                    }
                    else
                    {
                        MatchPath matchPath = new MatchPath
                        {
                            SourceNode = patternNode,
                            EdgeColumn = currentEdgeColumnRef,
                            EdgeAlias = edgeAlias,
                            BindNodeTableObjName =
                                new WSchemaObjectName(
                                    new Identifier {Value = schema},
                                    new Identifier {Value = bindTableName}
                                    ),
                            MinLength = currentEdgeColumnRef.MinLength,
                            MaxLength = currentEdgeColumnRef.MaxLength,
                            ReferencePathInfo = false,
                            AttributeValueDict = currentEdgeColumnRef.AttributeValueDict
                        };
                        _context.AddEdgeReference(matchPath);
                        pathDictionary[edgeAlias] = matchPath;
                        edge = matchPath;
                    }

                    if (preEdge != null)
                    {
                        preEdge.SinkNode = patternNode;
                        if (preEdge.HasReversedEdge)
                        {
                            //var preSourceNode = preEdge.SourceNode;
                            var preEdgeBindNodeTableObjName = preEdge.BindNodeTableObjName;
                            var preEdgeColName = preEdge.EdgeColumn.MultiPartIdentifier.Identifiers.Last().Value;
                            var preEdgeColumn =
                                columnsOfNodeTables[
                                    WNamedTableReference.SchemaNameToTuple(preEdgeBindNodeTableObjName)][
                                        preEdgeColName];
                            var isEdgeView = preEdgeColumn.Role == WNodeTableColumnRole.EdgeView;
                            var isNodeView =
                                _graphMetaData.NodeViewMapping.ContainsKey(
                                    WNamedTableReference.SchemaNameToTuple(patternNode.NodeTableObjectName));

                            reversedEdgeDict[preEdge.EdgeAlias].SourceNode = patternNode;
                            // [node/nodeView]-[edgeView]->[node/nodeView]
                            if (isEdgeView)
                            {
                                reversedEdgeDict[preEdge.EdgeAlias].BindNodeTableObjName = preEdgeBindNodeTableObjName;
                            }
                            // [node/nodeView]-[edge]->[nodeView]
                            else if (!isEdgeView && isNodeView)
                            {
                                reversedEdgeDict[preEdge.EdgeAlias].BindNodeTableObjName = new WSchemaObjectName(
                                    new Identifier { Value = "dbo" },
                                    new Identifier { Value = preEdgeColumn.EdgeInfo.SinkNodes.First() }
                                    );
                            }
                            else
                            {
                                reversedEdgeDict[preEdge.EdgeAlias].BindNodeTableObjName = new WSchemaObjectName(
                                    new Identifier { Value = schema },
                                    new Identifier { Value = bindTableName }
                                    );
                            }
                        }
                    }
                    preEdge = edge;

                    if (!parent.ContainsKey(currentNodeExposedName))
                        parent[currentNodeExposedName] = currentNodeExposedName;
                    if (!parent.ContainsKey(nextNodeExposedName))
                        parent[nextNodeExposedName] = nextNodeExposedName;

                    unionFind.Union(currentNodeExposedName, nextNodeExposedName);

                    patternNode.Neighbors.Add(edge);

                }
                var tailExposedName = path.Tail.BaseIdentifier.Value;
                var tailNode = nodes.GetOrCreate(tailExposedName);
                if (tailNode.NodeAlias == null)
                {
                    tailNode.NodeAlias = tailExposedName;
                    tailNode.Neighbors = new List<MatchEdge>();
                    var nodeTable = _context[tailExposedName] as WNamedTableReference;
                    if (nodeTable != null)
                    {
                        tailNode.NodeTableObjectName = nodeTable.TableObjectName;
                        if (tailNode.NodeTableObjectName.SchemaIdentifier == null)
                            tailNode.NodeTableObjectName.Identifiers.Insert(0, new Identifier {Value = "dbo"});
                    }
                }
                if (preEdge != null)
                {
                    preEdge.SinkNode = tailNode;
                    if (preEdge.HasReversedEdge)
                    {
                        var schema = tailNode.NodeTableObjectName.SchemaIdentifier.Value.ToLower();
                        var nodeTableName = tailNode.NodeTableObjectName.BaseIdentifier.Value;
                        //var preSourceNode = preEdge.SourceNode;
                        var preEdgeBindNodeTableObjName = preEdge.BindNodeTableObjName;
                        var preEdgeColName = preEdge.EdgeColumn.MultiPartIdentifier.Identifiers.Last().Value;
                        var preEdgeColumn =
                            columnsOfNodeTables[
                                WNamedTableReference.SchemaNameToTuple(preEdgeBindNodeTableObjName)][
                                    preEdgeColName];
                        var isEdgeView = preEdgeColumn.Role == WNodeTableColumnRole.EdgeView;
                        var isNodeView =
                            _graphMetaData.NodeViewMapping.ContainsKey(
                                WNamedTableReference.SchemaNameToTuple(tailNode.NodeTableObjectName));
                        reversedEdgeDict[preEdge.EdgeAlias].SourceNode = tailNode;
                        // [node/nodeView]-[edgeView]->[node/nodeView]
                        if (isEdgeView)
                        {
                            reversedEdgeDict[preEdge.EdgeAlias].BindNodeTableObjName = preEdgeBindNodeTableObjName;
                        }
                        // [node/nodeView]-[edge]->[nodeView]
                        else if (!isEdgeView && isNodeView)
                        {
                            reversedEdgeDict[preEdge.EdgeAlias].BindNodeTableObjName = new WSchemaObjectName(
                                new Identifier { Value = "dbo" },
                                new Identifier { Value = preEdgeColumn.EdgeInfo.SinkNodes.First() }
                                );
                        }
                        else
                        {
                            reversedEdgeDict[preEdge.EdgeAlias].BindNodeTableObjName = new WSchemaObjectName(
                                new Identifier { Value = schema },
                                new Identifier { Value = nodeTableName.ToLower() }
                                );
                        }
                    }
                }
            }

            // Puts nodes into subgraphs
            foreach (var node in nodes)
            {
                string root = unionFind.Find(node.Key);
                if (!subGrpahMap.ContainsKey(root))
                {
                    var subGraph = new ConnectedComponent();
                    subGraph.Nodes[node.Key] = node.Value;
                    foreach (var edge in node.Value.Neighbors)
                    {
                        subGraph.Edges[edge.EdgeAlias] = edge;
                    }
                    subGrpahMap[root] = subGraph;
                    connectedSubGraphs.Add(subGraph);
                    subGraph.IsTailNode[node.Value] = false;
                }
                else
                {
                    var subGraph = subGrpahMap[root];
                    subGraph.Nodes[node.Key] = node.Value;
                    foreach (var edge in node.Value.Neighbors)
                    {
                        subGraph.Edges[edge.EdgeAlias] = edge;
                    }
                    subGraph.IsTailNode[node.Value] = false;
                }
            }

            var graph = new MatchGraph
            {
                ReversedEdgeDict = reversedEdgeDict,
                ConnectedSubGraphs = connectedSubGraphs,
                SourceNodeStatisticsDict = new Dictionary<Tuple<string, bool>, Statistics>(),
            };
            unionFind.Parent = null;

            // When an edge in the MATCH clause is not associated with an alias,
            // assigns to it a default alias: sourceAlias_EdgeColumnName_sinkAlias.
            // Also rewrites edge attributes anywhere in the query that can be bound to this default alias.
            var replaceTableRefVisitor = new ReplaceEdgeReferenceVisitor();
            replaceTableRefVisitor.Invoke(query, edgeColumnToAliasesDict);

            // Rematerializes node tables in the MATCH clause which are defined in the upper-level context
            // and join them with the upper-level table references.
            RematerilizeExtrenalNodeTableReference(query, nodes);

            // Transforms the path reference in the SELECT elements into a
            // scalar function to display path information.
            TransformPathInfoDisplaySelectElement(query, pathDictionary);

            return graph;
        }
        /// <summary>
        /// Constructs the graph pattern specified by the MATCH clause. 
        /// The graph pattern may consist of multiple fully-connected sub-graphs.
        /// </summary>
        /// <param name="query">The SELECT query block</param>
        /// <returns>A graph object contains all the connected componeents</returns>
        private MatchGraph ConstructGraph(WSelectQueryBlock query)
        {
            if (query == null || query.MatchClause == null)
                return null;

            var unionFind = new UnionFind();
            var edgeColumnToAliasesDict = new Dictionary<string, List<string>>(StringComparer.OrdinalIgnoreCase);
            var pathDictionary = new Dictionary<string, MatchPath>(StringComparer.OrdinalIgnoreCase);
            var matchClause = query.MatchClause;
            var nodes = new Dictionary<string, MatchNode>(StringComparer.OrdinalIgnoreCase);
            var connectedSubGraphs = new List<ConnectedComponent>();
            var subGrpahMap = new Dictionary<string, ConnectedComponent>(StringComparer.OrdinalIgnoreCase);
            var parent = new Dictionary<string, string>(StringComparer.OrdinalIgnoreCase);
            unionFind.Parent = parent;

            // Constructs the graph pattern specified by the path expressions in the MATCH clause
            foreach (var path in matchClause.Paths)
            {
                var index = 0;
                MatchEdge preEdge = null;
                for (var count = path.PathEdgeList.Count; index < count; ++index)
                {
                    var currentNodeTableRef = path.PathEdgeList[index].Item1;
                    var currentEdgeColumnRef = path.PathEdgeList[index].Item2;
                    var currentNodeExposedName = currentNodeTableRef.BaseIdentifier.Value;
                    var nextNodeTableRef = index != count - 1
                        ? path.PathEdgeList[index + 1].Item1
                        : path.Tail;
                    var nextNodeExposedName = nextNodeTableRef.BaseIdentifier.Value;
                    var patternNode = nodes.GetOrCreate(currentNodeExposedName);
                    if (patternNode.NodeAlias == null)
                    {
                        patternNode.NodeAlias = currentNodeExposedName;
                        patternNode.Neighbors = new List<MatchEdge>();
                        patternNode.External = false;
                        var nodeTable = _context[currentNodeExposedName] as WNamedTableReference;
                        if (nodeTable != null)
                        {
                            patternNode.NodeTableObjectName = nodeTable.TableObjectName;
                            if (patternNode.NodeTableObjectName.SchemaIdentifier == null)
                                patternNode.NodeTableObjectName.Identifiers.Insert(0, new Identifier {Value = "dbo"});
                        }
                    }

                    string edgeAlias = currentEdgeColumnRef.Alias;
                    if (edgeAlias == null)
                    {
                        var currentEdgeName = currentEdgeColumnRef.MultiPartIdentifier.Identifiers.Last().Value;
                        edgeAlias = string.Format("{0}_{1}_{2}", currentNodeExposedName, currentEdgeName,
                            nextNodeExposedName);
                        if (edgeColumnToAliasesDict.ContainsKey(currentEdgeName))
                        {
                            edgeColumnToAliasesDict[currentEdgeName].Add(edgeAlias);
                        }
                        else
                        {
                            edgeColumnToAliasesDict.Add(currentEdgeName, new List<string> { edgeAlias });
                        }
                    }

                    Identifier edgeIdentifier = currentEdgeColumnRef.MultiPartIdentifier.Identifiers.Last();
                    string schema = patternNode.NodeTableObjectName.SchemaIdentifier.Value.ToLower();
                    string nodeTableName = patternNode.NodeTableObjectName.BaseIdentifier.Value;
                    string bindTableName =
                        _context.EdgeNodeBinding[
                            new Tuple<string, string>(nodeTableName.ToLower(), edgeIdentifier.Value.ToLower())].ToLower();
                    MatchEdge edge;
                    if (currentEdgeColumnRef.MinLength == 1 && currentEdgeColumnRef.MaxLength == 1)
                    {
                        edge = new MatchEdge
                        {
                            SourceNode = patternNode,
                            EdgeColumn = currentEdgeColumnRef,
                            EdgeAlias = edgeAlias,
                            BindNodeTableObjName =
                                new WSchemaObjectName(
                                    new Identifier {Value = schema},
                                    new Identifier {Value = bindTableName}
                                    ),
                        };
                        _context.AddEdgeReference(edge);
                    }
                    else
                    {
                        MatchPath matchPath = new MatchPath
                        {
                            SourceNode = patternNode,
                            EdgeColumn = currentEdgeColumnRef,
                            EdgeAlias = edgeAlias,
                            BindNodeTableObjName =
                                new WSchemaObjectName(
                                    new Identifier {Value = schema},
                                    new Identifier {Value = bindTableName}
                                    ),
                            MinLength = currentEdgeColumnRef.MinLength,
                            MaxLength = currentEdgeColumnRef.MaxLength,
                            ReferencePathInfo = false,
                            AttributeValueDict = currentEdgeColumnRef.AttributeValueDict
                        };
                        _context.AddEdgeReference(matchPath);
                        pathDictionary[edgeAlias] = matchPath;
                        edge = matchPath;
                    }

                    if (preEdge != null)
                    {
                        preEdge.SinkNode = patternNode;
                    }
                    preEdge = edge;

                    if (!parent.ContainsKey(currentNodeExposedName))
                        parent[currentNodeExposedName] = currentNodeExposedName;
                    if (!parent.ContainsKey(nextNodeExposedName))
                        parent[nextNodeExposedName] = nextNodeExposedName;

                    unionFind.Union(currentNodeExposedName, nextNodeExposedName);


                    patternNode.Neighbors.Add(edge);


                }
                var tailExposedName = path.Tail.BaseIdentifier.Value;
                var tailNode = nodes.GetOrCreate(tailExposedName);
                if (tailNode.NodeAlias == null)
                {
                    tailNode.NodeAlias = tailExposedName;
                    tailNode.Neighbors = new List<MatchEdge>();
                    var nodeTable = _context[tailExposedName] as WNamedTableReference;
                    if (nodeTable != null)
                    {
                        tailNode.NodeTableObjectName = nodeTable.TableObjectName;
                        if (tailNode.NodeTableObjectName.SchemaIdentifier == null)
                            tailNode.NodeTableObjectName.Identifiers.Insert(0, new Identifier {Value = "dbo"});
                    }
                }
                if (preEdge != null)
                    preEdge.SinkNode = tailNode;
            }

            // Puts nodes into subgraphs
            foreach (var node in nodes)
            {
                string root = unionFind.Find(node.Key);
                if (!subGrpahMap.ContainsKey(root))
                {
                    var subGraph = new ConnectedComponent();
                    subGraph.Nodes[node.Key] = node.Value;
                    foreach (var edge in node.Value.Neighbors)
                    {
                        subGraph.Edges[edge.EdgeAlias] = edge;
                    }
                    subGrpahMap[root] = subGraph;
                    connectedSubGraphs.Add(subGraph);
                    subGraph.IsTailNode[node.Value] = false;
                }
                else
                {
                    var subGraph = subGrpahMap[root];
                    subGraph.Nodes[node.Key] = node.Value;
                    foreach (var edge in node.Value.Neighbors)
                    {
                        subGraph.Edges[edge.EdgeAlias] = edge;
                    }
                    subGraph.IsTailNode[node.Value] = false;
                }
            }

            var graph = new MatchGraph
            {
                ConnectedSubGraphs = connectedSubGraphs,
            };
            unionFind.Parent = null;

            // When an edge in the MATCH clause is not associated with an alias, 
            // assigns to it a default alias: sourceAlias_EdgeColumnName_sinkAlias. 
            // Also rewrites edge attributes anywhere in the query that can be bound to this default alias. 
            var replaceTableRefVisitor = new ReplaceEdgeReferenceVisitor();
            replaceTableRefVisitor.Invoke(query, edgeColumnToAliasesDict);

            // Rematerializes node tables in the MATCH clause which are defined in the upper-level context
            // and join them with the upper-level table references.
            RematerilizeExtrenalNodeTableReference(query, nodes);

            // Transforms the path reference in the SELECT elements into a 
            // scalar function to display path information.
            TransformPathInfoDisplaySelectElement(query, pathDictionary);

            
            return graph;
        }