netron/source/dagre.js

var dagre = dagre || {};

// Dagre graph layout
// https://github.com/dagrejs/dagre
// https://github.com/dagrejs/graphlib

dagre.layout = (graph, options) => {
    options = options || {};
    // options.time = true;
    const time = (name, callback) => {
        const start = Date.now();
        const result = callback();
        const duration = Date.now() - start;
        if (options.time) {
            /* eslint-disable */
            console.log(name + ': ' + duration + 'ms');
            /* eslint-enable */
        }
        return result;
    };

    // Constructs a new graph from the input graph, which can be used for layout.
    // This process copies only whitelisted attributes from the input graph to the
    // layout graph. Thus this function serves as a good place to determine what
    // attributes can influence layout.
    const buildLayoutGraph = (graph) => {
        const g = new dagre.Graph({ compound: true });
        g.options = Object.assign({}, { ranksep: 50, edgesep: 20, nodesep: 50, rankdir: 'tb' }, graph.options);
        for (const node of graph.nodes.values()) {
            const v = node.v;
            const label = node.label;
            g.setNode(v, {
                width: label.width || 0,
                height: label.height || 0
            });
            g.setParent(v, graph.parent(v));
        }
        for (const e of graph.edges.values()) {
            const edge = e.label;
            g.setEdge(e.v, e.w, {
                minlen: edge.minlen || 1,
                weight: edge.weight || 1,
                width: edge.width || 0,
                height: edge.height || 0,
                labeloffset: edge.labeloffset || 10,
                labelpos: edge.labelpos || 'r'
            });
        }
        return g;
    };

    const runLayout = (g, time) => {
        let uniqueIdCounter = 0;
        const uniqueId = (prefix) => {
            const id = ++uniqueIdCounter;
            return prefix + id;
        };
        const flat = (list) => {
            if (Array.isArray(list) && list.every((item) => !Array.isArray(item))) {
                return list;
            }
            const target = [];
            for (const item of list) {
                if (!Array.isArray(item)) {
                    target.push(item);
                    continue;
                }
                for (const entry of item) {
                    target.push(entry);
                }
            }
            return target;
        };

        // Adds a dummy node to the graph and return v.
        const addDummyNode = (g, type, label, name) => {
            let v;
            do {
                v = uniqueId(name);
            } while (g.hasNode(v));
            label.dummy = type;
            g.setNode(v, label);
            return v;
        };

        const asNonCompoundGraph = (g) => {
            const graph = new dagre.Graph({});
            graph.options = g.options;
            for (const node of g.nodes.values()) {
                const v = node.v;
                if (g.children(v).length === 0) {
                    graph.setNode(v, node.label);
                }
            }
            for (const e of g.edges.values()) {
                graph.setEdge(e.v, e.w, e.label);
            }
            return graph;
        };

        const maxRank = (g) => {
            let rank = Number.NEGATIVE_INFINITY;
            for (const node of g.nodes.values()) {
                const x = node.label.rank;
                if (x !== undefined && x > rank) {
                    rank = x;
                }
            }
            return rank === Number.NEGATIVE_INFINITY ? undefined : rank;
        };

        // Given a DAG with each node assigned 'rank' and 'order' properties, this function will produce a matrix with the ids of each node.
        const buildLayerMatrix = (g) => {
            const rank = maxRank(g);
            const length = rank === undefined ? 0 : rank + 1;
            const layering = Array.from(new Array(length), () => []);
            for (const node of g.nodes.values()) {
                const label = node.label;
                const rank = label.rank;
                if (rank !== undefined) {
                    layering[rank][label.order] = node.v;
                }
            }
            return layering;
        };

        // This idea comes from the Gansner paper: to account for edge labels in our layout we split each rank in half by doubling minlen and halving ranksep.
        // Then we can place labels at these mid-points between nodes.
        // We also add some minimal padding to the width to push the label for the edge away from the edge itself a bit.
        const makeSpaceForEdgeLabels = (g) => {
            const graph = g.options;
            graph.ranksep /= 2;
            for (const e of g.edges.values()) {
                const edge = e.label;
                edge.minlen *= 2;
                if (edge.labelpos.toLowerCase() !== 'c') {
                    if (graph.rankdir === 'TB' || graph.rankdir === 'BT') {
                        edge.width += edge.labeloffset;
                    }
                    else {
                        edge.height += edge.labeloffset;
                    }
                }
            }
        };

        const removeSelfEdges = (g) => {
            for (const e of g.edges.values()) {
                if (e.v === e.w) {
                    const label = e.vNode.label;
                    if (!label.selfEdges) {
                        label.selfEdges = [];
                    }
                    label.selfEdges.push({ e: e, label: e.label });
                    g.removeEdge(e);
                }
            }
        };

        const acyclic_run = (g) => {
            const edges = [];
            const visited = new Set();
            const path = new Set();
            const stack = Array.from(g.nodes.keys()).reverse();
            while (stack.length > 0) {
                const v = stack.pop();
                if (!Array.isArray(v)) {
                    if (!visited.has(v)) {
                        visited.add(v);
                        path.add(v);
                        stack.push([ v ]);
                        const out = g.node(v).out;
                        for (let i = out.length - 1; i >= 0; i--) {
                            const e = out[i];
                            if (path.has(e.w)) {
                                edges.push(e);
                            }
                            stack.push(e.w);
                        }
                    }
                }
                else {
                    path.delete(v[0]);
                }
            }
            for (const e of edges) {
                const label = e.label;
                g.removeEdge(e);
                label.forwardName = e.name;
                label.reversed = true;
                g.setEdge(e.w, e.v, label, uniqueId('rev'));
            }
        };
        const acyclic_undo = (g) => {
            for (const e of g.edges.values()) {
                const edge = e.label;
                if (edge.reversed) {
                    edge.points.reverse();
                    g.removeEdge(e);
                    const forwardName = edge.forwardName;
                    delete edge.reversed;
                    delete edge.forwardName;
                    g.setEdge(e.w, e.v, edge, forwardName);
                }
            }
        };

        // Returns the amount of slack for the given edge.
        // The slack is defined as the difference between the length of the edge and its minimum length.
        const slack = (g, e) => {
            return e.wNode.label.rank - e.vNode.label.rank - e.label.minlen;
        };

        // Assigns a rank to each node in the input graph that respects the 'minlen' constraint specified on edges between nodes.
        // This basic structure is derived from Gansner, et al., 'A Technique for Drawing Directed Graphs.'
        //
        // Pre-conditions:
        //    1. Graph must be a connected DAG
        //    2. Graph nodes must be objects
        //    3. Graph edges must have 'weight' and 'minlen' attributes
        //
        // Post-conditions:
        //    1. Graph nodes will have a 'rank' attribute based on the results of the
        //       algorithm. Ranks can start at any index (including negative), we'll
        //       fix them up later.
        const rank = (g) => {
            // Constructs a spanning tree with tight edges and adjusted the input node's ranks to achieve this.
            // A tight edge is one that is has a length that matches its 'minlen' attribute.
            // The basic structure for this function is derived from Gansner, et al., 'A Technique for Drawing Directed Graphs.'
            //
            // Pre-conditions:
            //    1. Graph must be a DAG.
            //    2. Graph must be connected.
            //    3. Graph must have at least one node.
            //    5. Graph nodes must have been previously assigned a 'rank' property that respects the 'minlen' property of incident edges.
            //    6. Graph edges must have a 'minlen' property.
            //
            // Post-conditions:
            //    - Graph nodes will have their rank adjusted to ensure that all edges are tight.
            //
            // Returns a tree (undirected graph) that is constructed using only 'tight' edges.
            const feasibleTree = (g) => {
                const t = new dagre.Graph({ directed: false });
                // Choose arbitrary node from which to start our tree
                const start = g.nodes.keys().next().value;
                const size = g.nodes.size;
                t.setNode(start, {});
                // Finds a maximal tree of tight edges and returns the number of nodes in the tree.
                const tightTree = (t, g) => {
                    const stack = Array.from(t.nodes.keys()).reverse();
                    while (stack.length > 0) {
                        const v = stack.pop();
                        const node = g.node(v);
                        for (const e of node.in.concat(node.out)) {
                            const edgeV = e.v;
                            const w = (v === edgeV) ? e.w : edgeV;
                            if (!t.hasNode(w) && !slack(g, e)) {
                                t.setNode(w, {});
                                t.setEdge(v, w, {});
                                stack.push(w);
                            }
                        }
                    }
                    return t.nodes.size;
                };
                while (tightTree(t, g) < size) {
                    // Finds the edge with the smallest slack that is incident on tree and returns it.
                    let minKey = Number.MAX_SAFE_INTEGER;
                    let edge = undefined;
                    for (const e of g.edges.values()) {
                        if (t.hasNode(e.v) !== t.hasNode(e.w)) {
                            const key = slack(g, e);
                            if (key < minKey) {
                                minKey = key;
                                edge = e;
                            }
                        }
                    }
                    const delta = t.hasNode(edge.v) ? slack(g, edge) : -slack(g, edge);
                    for (const v of t.nodes.keys()) {
                        g.node(v).label.rank += delta;
                    }
                }
                return t;
            };
            // Initializes ranks for the input graph using the longest path algorithm.
            // This algorithm scales well and is fast in practice, it yields rather poor solutions.
            // Nodes are pushed to the lowest layer possible, leaving the bottom ranks wide and leaving edges longer than necessary.
            // However, due to its speed, this algorithm is good for getting an initial ranking that can be fed into other algorithms.
            //
            // This algorithm does not normalize layers because it will be used by other algorithms in most cases.
            // If using this algorithm directly, be sure to run normalize at the end.
            //
            // Pre-conditions:
            //    1. Input graph is a DAG.
            //    2. Input graph node labels can be assigned properties.
            //
            // Post-conditions:
            //    1. Each node will be assign an (unnormalized) 'rank' property.
            const longestPath = (g) => {
                const visited = new Set();
                const stack = [ Array.from(g.nodes.values()).filter((node) => node.in.length === 0).reverse() ];
                while (stack.length > 0) {
                    const current = stack[stack.length - 1];
                    if (Array.isArray(current)) {
                        const node = current.pop();
                        if (current.length === 0) {
                            stack.pop();
                        }
                        if (!visited.has(node)) {
                            visited.add(node);
                            const children = node.out.map((e) => e.wNode);
                            if (children.length > 0) {
                                stack.push(node);
                                stack.push(children.reverse());
                            }
                            else {
                                node.label.rank = 0;
                            }
                        }
                    }
                    else {
                        stack.pop();
                        let rank = Number.MAX_SAFE_INTEGER;
                        for (const e of current.out) {
                            rank = Math.min(rank, e.wNode.label.rank - e.label.minlen);
                        }
                        current.label.rank = rank;
                    }
                }
            };
            // The network simplex algorithm assigns ranks to each node in the input graph
            // and iteratively improves the ranking to reduce the length of edges.
            //
            // Preconditions:
            //    1. The input graph must be a DAG.
            //    2. All nodes in the graph must have an object value.
            //    3. All edges in the graph must have 'minlen' and 'weight' attributes.
            //
            // Postconditions:
            //    1. All nodes in the graph will have an assigned 'rank' attribute that has
            //       been optimized by the network simplex algorithm. Ranks start at 0.
            //
            // A rough sketch of the algorithm is as follows:
            //    1. Assign initial ranks to each node. We use the longest path algorithm,
            //       which assigns ranks to the lowest position possible. In general this
            //       leads to very wide bottom ranks and unnecessarily long edges.
            //    2. Construct a feasible tight tree. A tight tree is one such that all
            //       edges in the tree have no slack (difference between length of edge
            //       and minlen for the edge). This by itself greatly improves the assigned
            //       rankings by shorting edges.
            //    3. Iteratively find edges that have negative cut values. Generally a
            //       negative cut value indicates that the edge could be removed and a new
            //       tree edge could be added to produce a more compact graph.
            //
            // Much of the algorithms here are derived from Gansner, et al., 'A Technique
            // for Drawing Directed Graphs.' The structure of the file roughly follows the
            // structure of the overall algorithm.
            const networkSimplex = (g) => {
                // Returns a new graph with only simple edges. Handles aggregation of data associated with multi-edges.
                const simplify = (g) => {
                    const graph = new dagre.Graph();
                    graph.options = g.options;
                    for (const node of g.nodes.values()) {
                        graph.setNode(node.v, node.label);
                    }
                    for (const e of g.edges.values()) {
                        const simpleEdge =  graph.edge(e.v, e.w);
                        const simpleLabel = simpleEdge ? simpleEdge.label : { weight: 0, minlen: 1 };
                        const label = e.label;
                        graph.setEdge(e.v, e.w, {
                            weight: simpleLabel.weight + label.weight,
                            minlen: Math.max(simpleLabel.minlen, label.minlen)
                        });
                    }
                    return graph;
                };
                const initLowLimValues = (tree, root) => {
                    const dfs = (tree, visited, nextLim, v, parent) => {
                        const low = nextLim;
                        const label = tree.node(v).label;
                        visited.add(v);
                        for (const w of tree.neighbors(v)) {
                            if (!visited.has(w)) {
                                nextLim = dfs(tree, visited, nextLim, w, v);
                            }
                        }
                        label.low = low;
                        label.lim = nextLim++;
                        if (parent) {
                            label.parent = parent;
                        }
                        else {
                            // TODO should be able to remove this when we incrementally update low lim
                            delete label.parent;
                        }
                        return nextLim;
                    };
                    root = tree.nodes.keys().next().value;
                    const visited = new Set();
                    dfs(tree, visited, 1, root);
                };
                // Initializes cut values for all edges in the tree.
                const initCutValues = (t, g) => {
                    const vs = [];
                    const visited = new Set();
                    const stack = [ Array.from(t.nodes.keys()).reverse() ];
                    while (stack.length > 0) {
                        const current = stack[stack.length - 1];
                        if (Array.isArray(current)) {
                            const v = current.pop();
                            if (current.length === 0) {
                                stack.pop();
                            }
                            if (!visited.has(v)) {
                                visited.add(v);
                                const children = t.neighbors(v);
                                if (children.length > 0) {
                                    stack.push(v);
                                    stack.push(children.reverse());
                                }
                                else {
                                    vs.push(v);
                                }
                            }
                        }
                        else {
                            vs.push(stack.pop());
                        }
                    }
                    for (const v of vs.slice(0, vs.length - 1)) {
                        // Given the tight tree, its graph, and a child in the graph calculate and
                        // return the cut value for the edge between the child and its parent.
                        const childLabel = t.node(v).label;
                        const parent = childLabel.parent;
                        // The graph's view of the tree edge we're inspecting
                        const edge = g.edge(v, parent);
                        // True if the child is on the tail end of the edge in the directed graph
                        const childIsTail = edge ? true : false;
                        // The accumulated cut value for the edge between this node and its parent
                        const graphEdge = edge ? edge.label : g.edge(parent, v).label;
                        let cutValue = graphEdge.weight;
                        const node = g.node(v);
                        for (const e of node.in.concat(node.out)) {
                            const isOutEdge = e.v === v;
                            const other = isOutEdge ? e.w : e.v;
                            if (other !== parent) {
                                const pointsToHead = isOutEdge === childIsTail;
                                cutValue += pointsToHead ? e.label.weight : -e.label.weight;
                                const edge = t.edge(v, other);
                                if (edge) {
                                    const otherCutValue = edge.label.cutvalue;
                                    cutValue += pointsToHead ? -otherCutValue : otherCutValue;
                                }
                            }
                        }
                        t.edge(v, parent).label.cutvalue = cutValue;
                    }
                };
                const leaveEdge = (tree) => {
                    return Array.from(tree.edges.values()).find((e) => e.label.cutvalue < 0);
                };
                const enterEdge = (t, g, edge) => {
                    let v = edge.v;
                    let w = edge.w;
                    // For the rest of this function we assume that v is the tail and w is the
                    // head, so if we don't have this edge in the graph we should flip it to
                    // match the correct orientation.
                    if (!g.edge(v, w)) {
                        v = edge.w;
                        w = edge.v;
                    }
                    const vLabel = t.node(v).label;
                    const wLabel = t.node(w).label;
                    let tailLabel = vLabel;
                    let flip = false;
                    // If the root is in the tail of the edge then we need to flip the logic that
                    // checks for the head and tail nodes in the candidates function below.
                    if (vLabel.lim > wLabel.lim) {
                        tailLabel = wLabel;
                        flip = true;
                    }
                    // Returns true if the specified node is descendant of the root node per the assigned low and lim attributes in the tree.
                    const isDescendant = (vLabel, rootLabel) => {
                        return rootLabel.low <= vLabel.lim && vLabel.lim <= rootLabel.lim;
                    };
                    let minKey = Number.POSITIVE_INFINITY;
                    let minValue = undefined;
                    for (const edge of g.edges.values()) {
                        if (flip === isDescendant(t.node(edge.v).label, tailLabel) &&
                            flip !== isDescendant(t.node(edge.w).label, tailLabel)) {
                            const key = slack(g, edge);
                            if (key < minKey) {
                                minKey = key;
                                minValue = edge;
                            }
                        }
                    }
                    return minValue;
                };
                const exchangeEdges = (t, g, e, f) => {
                    t.removeEdge(e);
                    t.setEdge(f.v, f.w, {});
                    initLowLimValues(t);
                    initCutValues(t, g);
                    // update ranks
                    const root = Array.from(t.nodes.keys()).find((v) => !g.node(v).label.parent);
                    const stack = [ root ];
                    const visited = new Set();
                    while (stack.length > 0) {
                        const v = stack.pop();
                        if (!visited.has(v)) {
                            visited.add(v);
                            const neighbors = t.neighbors(v);
                            for (let i = neighbors.length - 1; i >= 0; i--) {
                                stack.push(neighbors[i]);
                            }
                        }
                    }
                    const vs = Array.from(visited);
                    for (const v of vs.slice(1)) {
                        const parent = t.node(v).label.parent;
                        let edge = g.edge(v, parent);
                        let flipped = false;
                        if (!edge) {
                            edge = g.edge(parent, v);
                            flipped = true;
                        }
                        g.node(v).label.rank = g.node(parent).label.rank + (flipped ? edge.label.minlen : -edge.label.minlen);
                    }
                };
                g = simplify(g);
                longestPath(g);
                const t = feasibleTree(g);
                initLowLimValues(t);
                initCutValues(t, g);
                let e;
                let f;
                while ((e = leaveEdge(t))) {
                    f = enterEdge(t, g, e);
                    exchangeEdges(t, g, e, f);
                }
            };
            switch (g.options.ranker) {
                case 'tight-tree':
                    longestPath(g);
                    feasibleTree(g);
                    break;
                case 'longest-path':
                    longestPath(g);
                    break;
                default:
                    networkSimplex(g);
                    break;
            }
        };

        // Creates temporary dummy nodes that capture the rank in which each edge's label is going to, if it has one of non-zero width and height.
        // We do this so that we can safely remove empty ranks while preserving balance for the label's position.
        const injectEdgeLabelProxies = (g) => {
            for (const e of g.edges.values()) {
                const edge = e.label;
                if (edge.width && edge.height) {
                    const v = e.vNode.label;
                    const w = e.wNode.label;
                    addDummyNode(g, 'edge-proxy', { rank: (w.rank - v.rank) / 2 + v.rank, e: e }, '_ep');
                }
            }
        };

        const removeEmptyRanks = (g) => {
            // Ranks may not start at 0, so we need to offset them
            if (g.nodes.size > 0) {
                let minRank = Number.MAX_SAFE_INTEGER;
                let maxRank = Number.MIN_SAFE_INTEGER;
                const nodes = Array.from(g.nodes.values());
                for (const node of nodes) {
                    const label = node.label;
                    if (label.rank !== undefined) {
                        minRank = Math.min(minRank, label.rank);
                        maxRank = Math.max(maxRank, label.rank);
                    }
                }
                const size = maxRank - minRank;
                if (size > 0) {
                    const layers = new Array(size);
                    for (const node of nodes) {
                        const label = node.label;
                        if (label.rank !== undefined) {
                            const rank = label.rank - minRank;
                            if (!layers[rank]) {
                                layers[rank] = [];
                            }
                            layers[rank].push(node.v);
                        }
                    }
                    let delta = 0;
                    const nodeRankFactor = g.options.nodeRankFactor;
                    for (let i = 0; i < layers.length; i++) {
                        const vs = layers[i];
                        if (vs === undefined && i % nodeRankFactor !== 0) {
                            delta--;
                        }
                        else if (delta && vs) {
                            for (const v of vs) {
                                g.node(v).label.rank += delta;
                            }
                        }
                    }
                }
            }
        };

        // A nesting graph creates dummy nodes for the tops and bottoms of subgraphs,
        // adds appropriate edges to ensure that all cluster nodes are placed between
        // these boundries, and ensures that the graph is connected.
        // In addition we ensure, through the use of the minlen property, that nodes
        // and subgraph border nodes do not end up on the same rank.
        //
        // Preconditions:
        //    1. Input graph is a DAG
        //    2. Nodes in the input graph has a minlen attribute
        //
        // Postconditions:
        //   1. Input graph is connected.
        //   2. Dummy nodes are added for the tops and bottoms of subgraphs.
        //   3. The minlen attribute for nodes is adjusted to ensure nodes do not
        //      get placed on the same rank as subgraph border nodes.
        //
        // The nesting graph idea comes from Sander, 'Layout of Compound Directed Graphs.'
        const nestingGraph_run = (g) => {
            const root = addDummyNode(g, 'root', {}, '_root');
            const treeDepths = (g) => {
                const depths = {};
                const dfs = (v, depth) => {
                    const children = g.children(v);
                    if (children && children.length > 0) {
                        for (const child of children) {
                            dfs(child, depth + 1);
                        }
                    }
                    depths[v] = depth;
                };
                for (const v of g.children()) {
                    dfs(v, 1);
                }
                return depths;
            };
            const dfs = (g, root, nodeSep, weight, height, depths, v) => {
                const children = g.children(v);
                if (!children.length) {
                    if (v !== root) {
                        g.setEdge(root, v, { weight: 0, minlen: nodeSep });
                    }
                    return;
                }
                const top = addDummyNode(g, 'border', { width: 0, height: 0 }, '_bt');
                const bottom = addDummyNode(g, 'border', { width: 0, height: 0 }, '_bb');
                const label = g.node(v).label;
                g.setParent(top, v);
                label.borderTop = top;
                g.setParent(bottom, v);
                label.borderBottom = bottom;
                for (const child of children) {
                    dfs(g, root, nodeSep, weight, height, depths, child);
                    const childNode = g.node(child).label;
                    const childTop = childNode.borderTop ? childNode.borderTop : child;
                    const childBottom = childNode.borderBottom ? childNode.borderBottom : child;
                    const thisWeight = childNode.borderTop ? weight : 2 * weight;
                    const minlen = childTop !== childBottom ? 1 : height - depths[v] + 1;
                    g.setEdge(top, childTop, { weight: thisWeight, minlen: minlen, nestingEdge: true });
                    g.setEdge(childBottom, bottom, { weight: thisWeight, minlen: minlen, nestingEdge: true });
                }
                if (!g.parent(v)) {
                    g.setEdge(root, top, { weight: 0, minlen: height + depths[v] });
                }
            };
            const depths = treeDepths(g);
            const height = Math.max(...Object.values(depths)) - 1; // Note: depths is an Object not an array
            const nodeSep = 2 * height + 1;
            g.options.nestingRoot = root;
            // Multiply minlen by nodeSep to align nodes on non-border ranks.
            for (const e of g.edges.values()) {
                e.label.minlen *= nodeSep;
            }
            // Calculate a weight that is sufficient to keep subgraphs vertically compact
            const weight = Array.from(g.edges.values()).reduce((acc, e) => acc + e.label.weight, 0) + 1;
            // Create border nodes and link them up
            for (const child of g.children()) {
                dfs(g, root, nodeSep, weight, height, depths, child);
            }
            // Save the multiplier for node layers for later removal of empty border layers.
            g.options.nodeRankFactor = nodeSep;
        };
        const nestingGraph_cleanup = (g) => {
            const graphLabel = g.options;
            g.removeNode(graphLabel.nestingRoot);
            delete graphLabel.nestingRoot;
            for (const e of g.edges.values()) {
                if (e.label.nestingEdge) {
                    g.removeEdge(e);
                }
            }
        };

        const assignRankMinMax = (g) => {
            // Adjusts the ranks for all nodes in the graph such that all nodes v have rank(v) >= 0 and at least one node w has rank(w) = 0.
            let min = Number.POSITIVE_INFINITY;
            for (const node of g.nodes.values()) {
                const rank = node.label.rank;
                if (rank !== undefined && rank < min) {
                    min = rank;
                }
            }
            for (const node of g.nodes.values()) {
                const label = node.label;
                if (label.rank !== undefined) {
                    label.rank -= min;
                }
            }
            let maxRank = 0;
            for (const node of g.nodes.values()) {
                const label = node.label;
                if (label.borderTop) {
                    label.minRank = g.node(label.borderTop).label.rank;
                    label.maxRank = g.node(label.borderBottom).label.rank;
                    maxRank = Math.max(maxRank, label.maxRank);
                }
            }
            g.options.maxRank = maxRank;
        };

        // Breaks any long edges in the graph into short segments that span 1 layer each.
        // This operation is undoable with the denormalize function.
        //
        // Pre-conditions:
        //   1. The input graph is a DAG.
        //   2. Each node in the graph has a 'rank' property.
        //
        // Post-condition:
        //   1. All edges in the graph have a length of 1.
        //   2. Dummy nodes are added where edges have been split into segments.
        //   3. The graph is augmented with a 'dummyChains' attribute which contains
        //      the first dummy in each chain of dummy nodes produced.
        const normalize = (g) => {
            g.options.dummyChains = [];
            for (const e of g.edges.values()) {
                let v = e.v;
                const w = e.w;
                const name = e.name;
                const edgeLabel = e.label;
                const labelRank = edgeLabel.labelRank;
                let vRank = g.node(v).label.rank;
                const wRank = g.node(w).label.rank;
                if (wRank !== vRank + 1) {
                    g.removeEdge(e);
                    let first = true;
                    vRank++;
                    while (vRank < wRank) {
                        edgeLabel.points = [];
                        delete e.key;
                        const attrs = {
                            width: 0, height: 0,
                            edgeLabel: edgeLabel,
                            edgeObj: e,
                            rank: vRank
                        };
                        const dummy = addDummyNode(g, 'edge', attrs, '_d');
                        if (vRank === labelRank) {
                            attrs.width = edgeLabel.width;
                            attrs.height = edgeLabel.height;
                            attrs.dummy = 'edge-label';
                            attrs.labelpos = edgeLabel.labelpos;
                        }
                        g.setEdge(v, dummy, { weight: edgeLabel.weight }, name);
                        if (first) {
                            g.options.dummyChains.push(dummy);
                            first = false;
                        }
                        v = dummy;
                        vRank++;
                    }
                    g.setEdge(v, w, { weight: edgeLabel.weight }, name);
                }
            }
        };

        const denormalize = (g) => {
            for (let v of g.options.dummyChains) {
                let label = g.node(v).label;
                const edgeLabel = label.edgeLabel;
                const e = label.edgeObj;
                g.setEdge(e.v, e.w, edgeLabel, e.name);
                while (label.dummy) {
                    const w = g.successors(v)[0];
                    g.removeNode(v);
                    edgeLabel.points.push({ x: label.x, y: label.y });
                    if (label.dummy === 'edge-label') {
                        edgeLabel.x = label.x;
                        edgeLabel.y = label.y;
                        edgeLabel.width = label.width;
                        edgeLabel.height = label.height;
                    }
                    v = w;
                    label = g.node(v).label;
                }
            }
        };

        const removeEdgeLabelProxies = (g) => {
            for (const node of g.nodes.values()) {
                const label = node.label;
                if (label.dummy === 'edge-proxy') {
                    label.e.label.labelRank = label.rank;
                    g.removeNode(node.v);
                }
            }
        };

        const parentDummyChains = (g) => {
            // Find a path from v to w through the lowest common ancestor (LCA). Return the full path and the LCA.
            const findPath = (g, postorderNums, v, w) => {
                const low = Math.min(postorderNums[v].low, postorderNums[w].low);
                const lim = Math.max(postorderNums[v].lim, postorderNums[w].lim);
                // Traverse up from v to find the LCA
                let parent = v;
                const vPath = [];
                do {
                    parent = g.parent(parent);
                    vPath.push(parent);
                }
                while (parent && (postorderNums[parent].low > low || lim > postorderNums[parent].lim));
                const lca = parent;
                // Traverse from w to LCA
                parent = w;
                const wPath = [];
                while ((parent = g.parent(parent)) !== lca) {
                    wPath.push(parent);
                }
                return { path: vPath.concat(wPath.reverse()), lca: lca };
            };
            const postorder = (g) => {
                const result = {};
                let lim = 0;
                const dfs = (v) => {
                    const low = lim;
                    for (const u of g.children(v)) {
                        dfs(u);
                    }
                    result[v] = { low: low, lim: lim++ };
                };
                for (const v of g.children()) {
                    dfs(v);
                }
                return result;
            };
            const postorderNums = postorder(g);
            for (let v of g.options.dummyChains || []) {
                const node = g.node(v).label;
                const edgeObj = node.edgeObj;
                const pathData = findPath(g, postorderNums, edgeObj.v, edgeObj.w);
                const path = pathData.path;
                const lca = pathData.lca;
                let pathIdx = 0;
                let pathV = path[pathIdx];
                let ascending = true;
                while (v !== edgeObj.w) {
                    const node = g.node(v).label;
                    if (ascending) {
                        while ((pathV = path[pathIdx]) !== lca && g.node(pathV).label.maxRank < node.rank) {
                            pathIdx++;
                        }
                        if (pathV === lca) {
                            ascending = false;
                        }
                    }
                    if (!ascending) {
                        while (pathIdx < path.length - 1 && g.node(path[pathIdx + 1]).label.minRank <= node.rank) {
                            pathIdx++;
                        }
                        pathV = path[pathIdx];
                    }
                    g.setParent(v, pathV);
                    v = g.successors(v)[0];
                }
            }
        };

        const addBorderSegments = (g) => {
            const addBorderNode = (g, prop, prefix, sg, sgNode, rank) => {
                const label = { width: 0, height: 0, rank: rank, borderType: prop };
                const prev = sgNode[prop][rank - 1];
                const curr = addDummyNode(g, 'border', label, prefix);
                sgNode[prop][rank] = curr;
                g.setParent(curr, sg);
                if (prev) {
                    g.setEdge(prev, curr, { weight: 1 });
                }
            };
            const queue = g.children();
            while (queue.length > 0) {
                const v = queue.shift();
                const node = g.node(v).label;
                if ('minRank' in node) {
                    node.borderLeft = [];
                    node.borderRight = [];
                    const maxRank = node.maxRank + 1;
                    for (let rank = node.minRank; rank < maxRank; rank++) {
                        addBorderNode(g, 'borderLeft', '_bl', v, node, rank);
                        addBorderNode(g, 'borderRight', '_br', v, node, rank);
                    }
                }
                const children = g.children(v);
                if (children.length) {
                    for (const v of children) {
                        queue.push(v);
                    }
                }
            }
        };

        // Applies heuristics to minimize edge crossings in the graph and sets the best order solution as an order attribute on each node.
        //
        // Pre-conditions:
        //    1. Graph must be DAG
        //    2. Graph nodes must have the 'rank' attribute
        //    3. Graph edges must have the 'weight' attribute
        //
        // Post-conditions:
        //    1. Graph nodes will have an 'order' attribute based on the results of the algorithm.
        const order = (g) => {
            const sortSubgraph = (g, v, cg, biasRight) => {
                // Given a list of entries of the form {v, barycenter, weight} and a constraint graph this function will resolve any conflicts between the constraint graph and the barycenters for the entries.
                // If the barycenters for an entry would violate a constraint in the constraint graph then we coalesce the nodes in the conflict into a new node that respects the contraint and aggregates barycenter and weight information.
                // This implementation is based on the description in Forster, 'A Fast and Simple Hueristic for Constrained Two-Level Crossing Reduction,' thought it differs in some specific details.
                //
                // Pre-conditions:
                //    1. Each entry has the form {v, barycenter, weight}, or if the node has no barycenter, then {v}.
                //
                // Returns:
                //    A new list of entries of the form {vs, i, barycenter, weight}.
                //    The list `vs` may either be a singleton or it may be an aggregation of nodes ordered such that they do not violate constraints from the constraint graph.
                //    The property `i` is the lowest original index of any of the elements in `vs`.
                const resolveConflicts = (entries, cg) => {
                    const mappedEntries = new Map();
                    for (let i = 0; i < entries.length; i++) {
                        const entry = entries[i];
                        const tmp = { indegree: 0, 'in': [], out: [], vs: [ entry.v ], i: i };
                        if (entry.barycenter !== undefined) {
                            tmp.barycenter = entry.barycenter;
                            tmp.weight = entry.weight;
                        }
                        mappedEntries.set(entry.v, tmp);
                    }
                    for (const e of cg.edges.values()) {
                        const entryV = mappedEntries.get(e.v);
                        const entryW = mappedEntries.get(e.w);
                        if (entryV && entryW) {
                            entryW.indegree++;
                            entryV.out.push(entryW);
                        }
                    }
                    const sourceSet = Array.from(mappedEntries.values()).filter((entry) => !entry.indegree);
                    const results = [];
                    function handleIn(vEntry) {
                        return function(uEntry) {
                            if (uEntry.merged) {
                                return;
                            }
                            if (uEntry.barycenter === undefined || vEntry.barycenter === undefined || uEntry.barycenter >= vEntry.barycenter) {
                                let sum = 0;
                                let weight = 0;
                                if (vEntry.weight) {
                                    sum += vEntry.barycenter * vEntry.weight;
                                    weight += vEntry.weight;
                                }
                                if (uEntry.weight) {
                                    sum += uEntry.barycenter * uEntry.weight;
                                    weight += uEntry.weight;
                                }
                                vEntry.vs = uEntry.vs.concat(vEntry.vs);
                                vEntry.barycenter = sum / weight;
                                vEntry.weight = weight;
                                vEntry.i = Math.min(uEntry.i, vEntry.i);
                                uEntry.merged = true;
                            }
                        };
                    }
                    function handleOut(vEntry) {
                        return function(wEntry) {
                            wEntry.in.push(vEntry);
                            if (--wEntry.indegree === 0) {
                                sourceSet.push(wEntry);
                            }
                        };
                    }
                    while (sourceSet.length) {
                        const entry = sourceSet.pop();
                        results.push(entry);
                        entry.in.reverse().forEach(handleIn(entry));
                        entry.out.forEach(handleOut(entry));
                    }
                    return results.filter((entry) => !entry.merged).map((entry) => {
                        const value = {
                            vs: entry.vs,
                            i: entry.i
                        };
                        if (entry.barycenter !== undefined) {
                            value.barycenter = entry.barycenter;
                        }
                        if (entry.weight !== undefined) {
                            value.weight = entry.weight;
                        }
                        return value;
                    });
                };
                const barycenter = (g, movable) => {
                    return (movable || []).map((v) => {
                        const inV = g.node(v).in;
                        if (!inV.length) {
                            return { v: v };
                        }
                        const result = inV.reduce((acc, e) => {
                            const edge = e.label;
                            const nodeU = e.vNode.label;
                            return {
                                sum: acc.sum + (edge.weight * nodeU.order),
                                weight: acc.weight + edge.weight
                            };
                        }, { sum: 0, weight: 0 });
                        return {
                            v: v,
                            barycenter: result.sum / result.weight,
                            weight: result.weight
                        };
                    });
                };
                const sort = (entries, biasRight) => {
                    const consumeUnsortable = (vs, unsortable, index) => {
                        let last;
                        while (unsortable.length && (last = unsortable[unsortable.length - 1]).i <= index) {
                            unsortable.pop();
                            vs.push(last.vs);
                            index++;
                        }
                        return index;
                    };
                    const compareWithBias = (bias) => {
                        return function(entryV, entryW) {
                            if (entryV.barycenter < entryW.barycenter) {
                                return -1;
                            }
                            else if (entryV.barycenter > entryW.barycenter) {
                                return 1;
                            }
                            return !bias ? entryV.i - entryW.i : entryW.i - entryV.i;
                        };
                    };
                    // partition
                    const parts = { lhs: [], rhs: [] };
                    for (const value of entries) {
                        if ('barycenter' in value) {
                            parts.lhs.push(value);
                        }
                        else {
                            parts.rhs.push(value);
                        }
                    }
                    const sortable = parts.lhs;
                    const unsortable = parts.rhs.sort((a, b) => -a.i + b.i);
                    const vs = [];
                    let sum = 0;
                    let weight = 0;
                    let vsIndex = 0;
                    sortable.sort(compareWithBias(!!biasRight));
                    vsIndex = consumeUnsortable(vs, unsortable, vsIndex);
                    for (const entry of sortable) {
                        vsIndex += entry.vs.length;
                        vs.push(entry.vs);
                        sum += entry.barycenter * entry.weight;
                        weight += entry.weight;
                        vsIndex = consumeUnsortable(vs, unsortable, vsIndex);
                    }
                    const result = { vs: flat(vs) };
                    if (weight) {
                        result.barycenter = sum / weight;
                        result.weight = weight;
                    }
                    return result;
                };
                const node = g.node(v);
                const bl = node && node.label ? node.label.borderLeft : undefined;
                const br = node && node.label ? node.label.borderRight: undefined;
                const subgraphs = {};
                const movable = bl ? g.children(v).filter((w) => w !== bl && w !== br) : g.children(v);
                const barycenters = barycenter(g, movable);
                for (const entry of barycenters) {
                    if (g.children(entry.v).length) {
                        const result = sortSubgraph(g, entry.v, cg, biasRight);
                        subgraphs[entry.v] = result;
                        if ('barycenter' in result) {
                            if (entry.barycenter !== undefined) {
                                entry.barycenter = (entry.barycenter * entry.weight + result.barycenter * result.weight) / (entry.weight + result.weight);
                                entry.weight += result.weight;
                            }
                            else {
                                entry.barycenter = result.barycenter;
                                entry.weight = result.weight;
                            }
                        }
                    }
                }
                const entries = resolveConflicts(barycenters, cg);
                // expand subgraphs
                for (const entry of entries) {
                    entry.vs = flat(entry.vs.map((v) => subgraphs[v] ? subgraphs[v].vs : v));
                }
                const result = sort(entries, biasRight);
                if (bl) {
                    result.vs = flat([bl, result.vs, br]);
                    if (g.predecessors(bl).length) {
                        const blPred = g.node(g.predecessors(bl)[0]).label;
                        const brPred = g.node(g.predecessors(br)[0]).label;
                        if (!('barycenter' in result)) {
                            result.barycenter = 0;
                            result.weight = 0;
                        }
                        result.barycenter = (result.barycenter * result.weight + blPred.order + brPred.order) / (result.weight + 2);
                        result.weight += 2;
                    }
                }
                return result;
            };
            const sweepLayerGraphs = (layerGraphs, biasRight) => {
                const cg = new dagre.Graph();
                for (const lg of layerGraphs) {
                    const root = lg.options.root;
                    const sorted = sortSubgraph(lg, root, cg, biasRight);
                    const vs = sorted.vs;
                    const length = vs.length;
                    for (let i = 0; i < length; i++) {
                        lg.node(vs[i]).label.order = i;
                    }
                    // add subgraph constraints
                    const prev = {};
                    let rootPrev;
                    let exit = false;
                    for (const v of vs) {
                        let child = lg.parent(v);
                        let prevChild;
                        while (child) {
                            const parent = lg.parent(child);
                            if (parent) {
                                prevChild = prev[parent];
                                prev[parent] = child;
                            }
                            else {
                                prevChild = rootPrev;
                                rootPrev = child;
                            }
                            if (prevChild && prevChild !== child) {
                                cg.setEdge(prevChild, child, null);
                                exit = true;
                                break;
                            }
                            child = parent;
                        }
                        if (exit) {
                            break;
                        }
                    }
                }
            };
            // A function that takes a layering (an array of layers, each with an array of
            // ordererd nodes) and a graph and returns a weighted crossing count.
            //
            // Pre-conditions:
            //    1. Input graph must be simple (not a multigraph), directed, and include
            //       only simple edges.
            //    2. Edges in the input graph must have assigned weights.
            //
            // Post-conditions:
            //    1. The graph and layering matrix are left unchanged.
            //
            // This algorithm is derived from Barth, et al., 'Bilayer Cross Counting.'
            const crossCount = (g, layering) => {
                let count = 0;
                for (let i = 1; i < layering.length; i++) {
                    const northLayer = layering[i - 1];
                    const southLayer = layering[i];
                    // Sort all of the edges between the north and south layers by their position in the north layer and then the south.
                    // Map these edges to the position of their head in the south layer.
                    const southPos = {};
                    for (let i = 0; i < southLayer.length; i++) {
                        southPos[southLayer[i]] = i;
                    }
                    const southEntries = [];
                    for (const v of northLayer) {
                        const entries = [];
                        for (const e of g.node(v).out) {
                            entries.push({
                                pos: southPos[e.w],
                                weight: e.label.weight
                            });
                        }
                        entries.sort((a, b) => a.pos - b.pos);
                        for (const entry of entries) {
                            southEntries.push(entry);
                        }
                    }
                    // Build the accumulator tree
                    let firstIndex = 1;
                    while (firstIndex < southLayer.length) {
                        firstIndex <<= 1;
                    }
                    const treeSize = 2 * firstIndex - 1;
                    firstIndex -= 1;
                    const tree = Array.from(new Array(treeSize), () => 0);
                    // Calculate the weighted crossings
                    for (const entry of southEntries) {
                        let index = entry.pos + firstIndex;
                        tree[index] += entry.weight;
                        let weightSum = 0;
                        while (index > 0) {
                            if (index % 2) {
                                weightSum += tree[index + 1];
                            }
                            index = (index - 1) >> 1;
                            tree[index] += entry.weight;
                        }
                        count += entry.weight * weightSum;
                    }
                }
                return count;
            };
            // Assigns an initial order value for each node by performing a DFS search
            // starting from nodes in the first rank. Nodes are assigned an order in their
            // rank as they are first visited.
            //
            // This approach comes from Gansner, et al., 'A Technique for Drawing Directed
            // Graphs.'
            //
            // Returns a layering matrix with an array per layer and each layer sorted by
            // the order of its nodes.
            const initOrder = (g) => {
                const visited = new Set();
                const nodes = Array.from(g.nodes.values()).filter((node) => g.children(node.v).length === 0);
                let maxRank = undefined;
                for (const node of nodes) {
                    const rank = node.label.rank;
                    if (maxRank === undefined || (rank !== undefined && rank > maxRank)) {
                        maxRank = rank;
                    }
                }
                if (maxRank !== undefined) {
                    const layers = Array.from(new Array(maxRank + 1), () => []);
                    const queue = nodes.sort((a, b) => a.label.rank - b.label.rank).map((node) => node.v).reverse();
                    while (queue.length > 0) {
                        const v = queue.shift();
                        if (!visited.has(v)) {
                            visited.add(v);
                            const rank = g.node(v).label.rank;
                            layers[rank].push(v);
                            for (const w of g.successors(v)) {
                                queue.push(w);
                            }
                        }
                    }
                    return layers;
                }
                return [];
            };
            // Constructs a graph that can be used to sort a layer of nodes.
            // The graph will contain all base and subgraph nodes from the request layer in their original
            // hierarchy and any edges that are incident on these nodes and are of the type requested by the 'relationship' parameter.
            //
            // Nodes from the requested rank that do not have parents are assigned a root node in the output graph,
            // which is set in the root graph attribute.
            // This makes it easy to walk the hierarchy of movable nodes during ordering.
            //
            // Pre-conditions:
            //    1. Input graph is a DAG
            //    2. Base nodes in the input graph have a rank attribute
            //    3. Subgraph nodes in the input graph has minRank and maxRank attributes
            //    4. Edges have an assigned weight
            //
            // Post-conditions:
            //    1. Output graph has all nodes in the movable rank with preserved hierarchy.
            //    2. Root nodes in the movable layer are made children of the node
            //       indicated by the root attribute of the graph.
            //    3. Non-movable nodes incident on movable nodes, selected by the
            //       relationship parameter, are included in the graph (without hierarchy).
            //    4. Edges incident on movable nodes, selected by the relationship parameter, are added to the output graph.
            //    5. The weights for copied edges are aggregated as need, since the output graph is not a multi-graph.
            const buildLayerGraph = (g, nodes, rank, relationship) => {
                let root;
                while (g.hasNode((root = uniqueId('_root')))) {
                    // continue
                }
                const graph = new dagre.Graph({ compound: true });
                graph.options = { root: root };
                graph.setDefaultNodeLabel((v) => {
                    const node = g.node(v);
                    return node ? node.label : undefined;
                });
                const length = nodes.length;
                let i = 0;
                while (i < length) {
                    const node = nodes[i++];
                    const label = node.label;
                    if (label.rank === rank || 'minRank' in label && 'maxRank' in label && label.minRank <= rank && rank <= label.maxRank) {
                        const v = node.v;
                        graph.setNode(v);
                        const parent = g.parent(v);
                        graph.setParent(v, parent || root);
                        // This assumes we have only short edges!
                        if (relationship) {
                            for (const e of node.in) {
                                graph.setEdge(e.v, v, { weight: e.label.weight });
                            }
                        }
                        else {
                            for (const e of node.out) {
                                graph.setEdge(e.w, v, { weight: e.label.weight });
                            }
                        }
                        if ('minRank' in label) {
                            graph.setNode(v, {
                                borderLeft: label.borderLeft[rank],
                                borderRight: label.borderRight[rank]
                            });
                        }
                    }
                }
                return graph;
            };
            let layering = initOrder(g);
            const assignOrder = (g, layering) => {
                for (const layer of layering) {
                    for (let i = 0; i < layer.length; i++) {
                        g.node(layer[i]).label.order = i;
                    }
                }
            };
            assignOrder(g, layering);
            const rank = maxRank(g) || 0;
            const downLayerGraphs = new Array(rank);
            const upLayerGraphs = new Array(rank);
            const nodes = Array.from(g.nodes.values());
            for (let i = 0; i < rank; i++) {
                downLayerGraphs[i] = buildLayerGraph(g, nodes, i + 1, true);
                upLayerGraphs[i] = buildLayerGraph(g, nodes, rank - i - 1, false);
            }
            let bestCC = Number.POSITIVE_INFINITY;
            let best;
            for (let i = 0, lastBest = 0; lastBest < 4; ++i, ++lastBest) {
                sweepLayerGraphs(i % 2 ? downLayerGraphs : upLayerGraphs, i % 4 >= 2);
                layering = buildLayerMatrix(g);
                const cc = crossCount(g, layering);
                if (cc < bestCC) {
                    lastBest = 0;
                    const length = layering.length;
                    best = new Array(length);
                    for (let j = 0; j < length; j++) {
                        best[j] = layering[j].slice();
                    }
                    bestCC = cc;
                }
            }
            assignOrder(g, best);
        };

        const insertSelfEdges = (g) => {
            const layers = buildLayerMatrix(g);
            for (const layer of layers) {
                let orderShift = 0;
                layer.forEach(function(v, i) {
                    const label = g.node(v).label;
                    label.order = i + orderShift;
                    if (label.selfEdges) {
                        for (const selfEdge of label.selfEdges) {
                            addDummyNode(g, 'selfedge', {
                                width: selfEdge.label.width,
                                height: selfEdge.label.height,
                                rank: label.rank,
                                order: i + (++orderShift),
                                e: selfEdge.e,
                                label: selfEdge.label
                            }, '_se');
                        }
                        delete label.selfEdges;
                    }
                });
            }
        };

        const coordinateSystem_swapWidthHeight = (g) => {
            for (const node of g.nodes.values()) {
                const label = node.label;
                const w = label.width;
                label.width = label.height;
                label.height = w;
            }
            for (const e of g.edges.values()) {
                const label = e.label;
                const w = label.width;
                label.width = label.height;
                label.height = w;
            }
        };
        const coordinateSystem_adjust = (g) => {
            const rankDir = g.options.rankdir.toLowerCase();
            if (rankDir === 'lr' || rankDir === 'rl') {
                coordinateSystem_swapWidthHeight(g);
            }
        };
        const coordinateSystem_undo = (g) => {
            const rankDir = g.options.rankdir.toLowerCase();
            if (rankDir === 'bt' || rankDir === 'rl') {
                for (const node of g.nodes.values()) {
                    node.label.y = -node.label.y;
                }
                for (const e of g.edges.values()) {
                    const edge = e.label;
                    for (const attr of edge.points) {
                        attr.y = -attr.y;
                    }
                    if ('y' in edge) {
                        edge.y = -edge.y;
                    }
                }
            }
            if (rankDir === 'lr' || rankDir === 'rl') {
                const swapXYOne = (attrs) => {
                    const x = attrs.x;
                    attrs.x = attrs.y;
                    attrs.y = x;
                };
                for (const node of g.nodes.values()) {
                    swapXYOne(node.label);
                }
                for (const e of g.edges.values()) {
                    const edge = e.label;
                    for (const e of edge.points) {
                        swapXYOne(e);
                    }
                    if (edge.x !== undefined) {
                        swapXYOne(edge);
                    }
                }
                coordinateSystem_swapWidthHeight(g);
            }
        };

        const position = (g) => {
            const addConflict = (conflicts, v, w) => {
                if (v > w) {
                    const tmp = v;
                    v = w;
                    w = tmp;
                }
                let conflictsV = conflicts[v];
                if (!conflictsV) {
                    conflicts[v] = conflictsV = {};
                }
                conflictsV[w] = true;
            };
            const hasConflict = (conflicts, v, w) => {
                if (v > w) {
                    const tmp = v;
                    v = w;
                    w = tmp;
                }
                return conflicts[v] && w in conflicts[v];
            };
            const buildBlockGraph = (g, layering, root, reverseSep) => {
                const nodeSep = g.options.nodesep;
                const edgeSep = g.options.edgesep;
                const blockGraph = new dagre.Graph();
                for (const layer of layering) {
                    let u;
                    for (const v of layer) {
                        const vRoot = root[v];
                        blockGraph.setNode(vRoot, {});
                        if (u) {
                            const uRoot = root[u];
                            const vLabel = g.node(v).label;
                            const wLabel = g.node(u).label;
                            let sum = 0;
                            let delta;
                            sum += vLabel.width / 2;
                            if ('labelpos' in vLabel) {
                                switch (vLabel.labelpos) {
                                    case 'l': delta = -vLabel.width / 2; break;
                                    case 'r': delta = vLabel.width / 2; break;
                                    default: throw new dagre.Error("Unsupported label position '" + vLabel.labelpos + "'.");
                                }
                            }
                            if (delta) {
                                sum += reverseSep ? delta : -delta;
                            }
                            delta = 0;
                            sum += (vLabel.dummy ? edgeSep : nodeSep) / 2;
                            sum += (wLabel.dummy ? edgeSep : nodeSep) / 2;
                            sum += wLabel.width / 2;
                            if ('labelpos' in wLabel) {
                                switch (wLabel.labelpos) {
                                    case 'l': delta = wLabel.width / 2; break;
                                    case 'r': delta = -wLabel.width / 2; break;
                                    default: throw new dagre.Error("Unsupported label position '" + wLabel.labelpos + "'.");
                                }
                            }
                            if (delta) {
                                sum += reverseSep ? delta : -delta;
                            }
                            const edge = blockGraph.edge(uRoot, vRoot);
                            const max = Math.max(sum, edge ? edge.label : 0);
                            if (edge) {
                                edge.label = max;
                            }
                            else {
                                blockGraph.setEdge(uRoot, vRoot, max);
                            }
                        }
                        u = v;
                    }
                }
                return blockGraph;
            };
            // Try to align nodes into vertical 'blocks' where possible.
            // This algorithm attempts to align a node with one of its median neighbors.
            // If the edge connecting a neighbor is a type-1 conflict then we ignore that possibility.
            // If a previous node has already formed a block with a node after the node we're trying to form a block with,
            // we also ignore that possibility - our blocks would be split in that scenario.
            const verticalAlignment = (layering, conflicts, neighborFn) => {
                const root = {};
                const align = {};
                const pos = {};
                // We cache the position here based on the layering because the graph and layering may be out of sync.
                // The layering matrix is manipulated to generate different extreme alignments.
                for (const layer of layering) {
                    let order = 0;
                    for (const v of layer) {
                        root[v] = v;
                        align[v] = v;
                        pos[v] = order;
                        order++;
                    }
                }
                for (const layer of layering) {
                    let prevIdx = -1;
                    for (const v of layer) {
                        let ws = neighborFn(v);
                        if (ws.length > 0) {
                            ws = ws.sort((a, b) => pos[a] - pos[b]);
                            const mp = (ws.length - 1) / 2.0;
                            const il = Math.ceil(mp);
                            for (let i = Math.floor(mp); i <= il; i++) {
                                const w = ws[i];
                                if (align[v] === v && prevIdx < pos[w] && !hasConflict(conflicts, v, w)) {
                                    align[w] = v;
                                    align[v] = root[v] = root[w];
                                    prevIdx = pos[w];
                                }
                            }
                        }
                    }
                }
                return { root: root, align: align };
            };
            const horizontalCompaction = (g, layering, root, align, reverseSep) => {
                // This portion of the algorithm differs from BK due to a number of problems.
                // Instead of their algorithm we construct a new block graph and do two sweeps.
                const blockG = buildBlockGraph(g, layering, root, reverseSep);
                const borderType = reverseSep ? 'borderLeft' : 'borderRight';
                const xs = {};
                // First pass, places blocks with the smallest possible coordinates.
                if (blockG.nodes.size > 0) {
                    const stack = Array.from(blockG.nodes.keys());
                    const visited = new Set();
                    while (stack.length > 0) {
                        const v = stack.pop();
                        if (visited.has(v)) {
                            let max = 0;
                            for (const e of blockG.node(v).in) {
                                max = Math.max(max, xs[e.v] + e.label);
                            }
                            xs[v] = max;
                        }
                        else {
                            visited.add(v);
                            stack.push(v);
                            for (const w of blockG.predecessors(v)) {
                                stack.push(w);
                            }
                        }
                    }
                }
                // Second pass, removes unused space by moving blocks to the greatest coordinates without violating separation.
                if (blockG.nodes.size > 0) {
                    const stack = Array.from(blockG.nodes.keys());
                    const visited = new Set();
                    while (stack.length > 0) {
                        const v = stack.pop();
                        if (visited.has(v)) {
                            let min = Number.POSITIVE_INFINITY;
                            for (const e of blockG.node(v).out) {
                                min = Math.min(min, xs[e.w] - e.label);
                            }
                            const label = g.node(v).label;
                            if (min !== Number.POSITIVE_INFINITY && label.borderType !== borderType) {
                                xs[v] = Math.max(xs[v], min);
                            }
                        }
                        else {
                            visited.add(v);
                            stack.push(v);
                            for (const w of blockG.successors(v)) {
                                stack.push(w);
                            }
                        }
                    }
                }
                // Assign x coordinates to all nodes
                for (const v of Object.values(align)) {
                    xs[v] = xs[root[v]];
                }
                return xs;
            };
            // Marks all edges in the graph with a type-1 conflict with the 'type1Conflict' property.
            // A type-1 conflict is one where a non-inner segment crosses an inner segment.
            // An inner segment is an edge with both incident nodes marked with the 'dummy' property.
            //
            // This algorithm scans layer by layer, starting with the second, for type-1
            // conflicts between the current layer and the previous layer. For each layer
            // it scans the nodes from left to right until it reaches one that is incident
            // on an inner segment. It then scans predecessors to determine if they have
            // edges that cross that inner segment. At the end a final scan is done for all
            // nodes on the current rank to see if they cross the last visited inner segment.
            //
            // This algorithm (safely) assumes that a dummy node will only be incident on a
            // single node in the layers being scanned.
            const findType1Conflicts = (g, layering) => {
                const conflicts = {};
                if (layering.length > 0) {
                    let prev = layering[0];
                    for (let k = 1; k < layering.length; k++) {
                        const layer = layering[k];
                        // last visited node in the previous layer that is incident on an inner segment.
                        let k0 = 0;
                        // Tracks the last node in this layer scanned for crossings with a type-1 segment.
                        let scanPos = 0;
                        const prevLayerLength = prev.length;
                        const lastNode = layer[layer.length - 1];
                        for (let i = 0; i < layer.length; i++) {
                            const v = layer[i];
                            const w = g.node(v).label.dummy ? g.predecessors(v).find((u) => g.node(u).label.dummy) : null;
                            if (w || v === lastNode) {
                                const k1 = w ? g.node(w).label.order : prevLayerLength;
                                for (const scanNode of layer.slice(scanPos, i + 1)) {
                                // for (const scanNode of layer.slice(scanPos, scanPos + 1)) {
                                    for (const u of g.predecessors(scanNode)) {
                                        const uLabel = g.node(u).label;
                                        const uPos = uLabel.order;
                                        if ((uPos < k0 || k1 < uPos) && !(uLabel.dummy && g.node(scanNode).label.dummy)) {
                                            addConflict(conflicts, u, scanNode);
                                        }
                                    }
                                }
                                // scanPos += 1;
                                scanPos = i + 1;
                                k0 = k1;
                            }
                        }
                        prev = layer;
                    }
                }
                return conflicts;
            };
            const findType2Conflicts = (g, layering) => {
                const conflicts = {};
                const scan = (south, southPos, southEnd, prevNorthBorder, nextNorthBorder) => {
                    let v;
                    for (let i = southPos; i < southEnd; i++) {
                        v = south[i];
                        if (g.node(v).labeldummy) {
                            for (const u of g.predecessors(v)) {
                                const uNode = g.node(u).label;
                                if (uNode.dummy && (uNode.order < prevNorthBorder || uNode.order > nextNorthBorder)) {
                                    addConflict(conflicts, u, v);
                                }
                            }
                        }
                    }
                };
                if (layering.length > 0) {
                    let north = layering[0];
                    for (let i = 1; i < layering.length; i++) {
                        const south = layering[i];
                        let prevNorthPos = -1;
                        let nextNorthPos;
                        let southPos = 0;
                        south.forEach(function(v, southLookahead) {
                            if (g.node(v).label.dummy === 'border') {
                                const predecessors = g.predecessors(v);
                                if (predecessors.length) {
                                    nextNorthPos = g.node(predecessors[0]).label.order;
                                    scan(south, southPos, southLookahead, prevNorthPos, nextNorthPos);
                                    southPos = southLookahead;
                                    prevNorthPos = nextNorthPos;
                                }
                            }
                            scan(south, southPos, south.length, nextNorthPos, north.length);
                        });
                        north = south;
                    }
                }
                return conflicts;
            };

            g = asNonCompoundGraph(g);
            const layering = buildLayerMatrix(g);
            const ranksep = g.options.ranksep;
            // Assign y-coordinate based on rank
            let y = 0;
            for (const layer of layering) {
                const maxHeight = layer.reduce((a, v) => Math.max(a, g.node(v).label.height), 0);
                for (const v of layer) {
                    g.node(v).label.y = y + maxHeight / 2;
                }
                y += maxHeight + ranksep;
            }
            // Coordinate assignment based on Brandes and Köpf, 'Fast and Simple Horizontal Coordinate Assignment.'
            const conflicts = Object.assign(findType1Conflicts(g, layering), findType2Conflicts(g, layering));
            const xss = {};
            for (const vertical of ['u', 'd']) {
                let adjustedLayering = vertical === 'u' ? layering : Object.values(layering).reverse();
                for (const horizontal of ['l', 'r']) {
                    if (horizontal === 'r') {
                        adjustedLayering = adjustedLayering.map((layer) => Object.values(layer).reverse());
                    }
                    const neighborFn = (vertical === 'u' ? g.predecessors : g.successors).bind(g);
                    const align = verticalAlignment(adjustedLayering, conflicts, neighborFn);
                    const xs = horizontalCompaction(g, adjustedLayering, align.root, align.align, horizontal === 'r');
                    if (horizontal === 'r') {
                        for (const entry of Object.entries(xs)) {
                            xs[entry[0]] = -entry[1];
                        }
                    }
                    xss[vertical + horizontal] = xs;
                }
            }
            // Find smallest width alignment: Returns the alignment that has the smallest width of the given alignments.
            let minWidth = Number.POSITIVE_INFINITY;
            let minValue = undefined;
            for (const xs of Object.values(xss)) {
                let max = Number.NEGATIVE_INFINITY;
                let min = Number.POSITIVE_INFINITY;
                for (const entry of Object.entries(xs)) {
                    const v = entry[0];
                    const x = entry[1];
                    const halfWidth = g.node(v).label.width / 2;
                    max = Math.max(x + halfWidth, max);
                    min = Math.min(x - halfWidth, min);
                }
                const width = max - min;
                if (width < minWidth) {
                    minWidth = width;
                    minValue = xs;
                }
            }
            // Align the coordinates of each of the layout alignments such that
            // left-biased alignments have their minimum coordinate at the same point as
            // the minimum coordinate of the smallest width alignment and right-biased
            // alignments have their maximum coordinate at the same point as the maximum
            // coordinate of the smallest width alignment.
            const alignTo = minValue;
            const range = (values) => {
                let min = Number.POSITIVE_INFINITY;
                let max = Number.NEGATIVE_INFINITY;
                for (const value of values) {
                    if (value < min) {
                        min = value;
                    }
                    if (value > max) {
                        max = value;
                    }
                }
                return [ min, max ];
            };
            const alignToRange = range(Object.values(alignTo));
            for (const vertical of ['u', 'd']) {
                for (const horizontal of ['l', 'r']) {
                    const alignment = vertical + horizontal;
                    const xs = xss[alignment];
                    let delta;
                    if (xs !== alignTo) {
                        const vsValsRange = range(Object.values(xs));
                        delta = horizontal === 'l' ? alignToRange[0] - vsValsRange[0] : alignToRange[1] - vsValsRange[1];
                        if (delta) {
                            const list = {};
                            for (const key of Object.keys(xs)) {
                                list[key] = xs[key] + delta;
                            }
                            xss[alignment] = list;
                        }
                    }
                }
            }
            // balance
            const align = g.options.align;
            if (align) {
                const xs = xss[align.toLowerCase()];
                for (const v of Object.keys(xss.ul)) {
                    g.node(v).label.x = xs[v];
                }
            }
            else {
                for (const v of Object.keys(xss.ul)) {
                    const xs = [ xss.ul[v], xss.ur[v], xss.dl[v], xss.dr[v] ].sort((a, b) => a - b);
                    g.node(v).label.x = (xs[1] + xs[2]) / 2;
                }
            }
        };

        const positionSelfEdges = (g) => {
            for (const node of g.nodes.values()) {
                const label = node.label;
                if (label.dummy === 'selfedge') {
                    const v = node.v;
                    const selfNode = g.node(label.e.v).label;
                    const x = selfNode.x + selfNode.width / 2;
                    const y = selfNode.y;
                    const dx = label.x - x;
                    const dy = selfNode.height / 2;
                    g.setEdge(label.e.v, label.e.w, label.label);
                    g.removeNode(v);
                    label.label.points = [
                        { x: x + 2 * dx / 3, y: y - dy },
                        { x: x + 5 * dx / 6, y: y - dy },
                        { x: x +     dx    , y: y },
                        { x: x + 5 * dx / 6, y: y + dy },
                        { x: x + 2 * dx / 3, y: y + dy }
                    ];
                    label.label.x = label.x;
                    label.label.y = label.y;
                }
            }
        };

        const removeBorderNodes = (g) => {
            for (const node of g.nodes.values()) {
                const v = node.v;
                if (g.children(v).length) {
                    const label = node.label;
                    const t = g.node(label.borderTop).label;
                    const b = g.node(label.borderBottom).label;
                    const l = g.node(label.borderLeft[label.borderLeft.length - 1]).label;
                    const r = g.node(label.borderRight[label.borderRight.length - 1]).label;
                    label.width = Math.abs(r.x - l.x);
                    label.height = Math.abs(b.y - t.y);
                    label.x = l.x + label.width / 2;
                    label.y = t.y + label.height / 2;
                }
            }
            for (const node of g.nodes.values()) {
                if (node.label.dummy === 'border') {
                    g.removeNode(node.v);
                }
            }
        };

        const fixupEdgeLabelCoords = (g) => {
            for (const e of g.edges.values()) {
                const edge = e.label;
                if ('x' in edge) {
                    if (edge.labelpos === 'l' || edge.labelpos === 'r') {
                        edge.width -= edge.labeloffset;
                    }
                    switch (edge.labelpos) {
                        case 'l': edge.x -= edge.width / 2 + edge.labeloffset; break;
                        case 'r': edge.x += edge.width / 2 + edge.labeloffset; break;
                        default: throw new dagre.Error("Unsupported label position '" + edge.labelpos + "'.");
                    }
                }
            }
        };

        const translateGraph = (g) => {
            let minX = Number.POSITIVE_INFINITY;
            let maxX = 0;
            let minY = Number.POSITIVE_INFINITY;
            let maxY = 0;
            const getExtremes = (attrs) => {
                const x = attrs.x;
                const y = attrs.y;
                const w = attrs.width;
                const h = attrs.height;
                minX = Math.min(minX, x - w / 2);
                maxX = Math.max(maxX, x + w / 2);
                minY = Math.min(minY, y - h / 2);
                maxY = Math.max(maxY, y + h / 2);
            };
            for (const node of g.nodes.values()) {
                getExtremes(node.label);
            }
            for (const e of g.edges.values()) {
                const edge = e.label;
                if ('x' in edge) {
                    getExtremes(edge);
                }
            }
            for (const node of g.nodes.values()) {
                node.label.x -= minX;
                node.label.y -= minY;
            }
            for (const e of g.edges.values()) {
                const edge = e.label;
                for (const p of edge.points) {
                    p.x -= minX;
                    p.y -= minY;
                }
                if ('x' in edge) {
                    edge.x -= minX;
                }
                if ('y' in edge) {
                    edge.y -= minY;
                }
            }
            const graphLabel = g.options;
            graphLabel.width = maxX - minX;
            graphLabel.height = maxY - minY;
        };

        const assignNodeIntersects = (g) => {
            // Finds where a line starting at point ({x, y}) would intersect a rectangle
            // ({x, y, width, height}) if it were pointing at the rectangle's center.
            const intersectRect = (rect, point) => {
                const x = rect.x;
                const y = rect.y;
                // Rectangle intersection algorithm from: http://math.stackexchange.com/questions/108113/find-edge-between-two-boxes
                const dx = point.x - x;
                const dy = point.y - y;
                if (dx === 0 && dy === 0) {
                    throw new Error('Not possible to find intersection inside of the rectangle');
                }
                let w = rect.width / 2;
                let h = rect.height / 2;
                if (Math.abs(dy) * w > Math.abs(dx) * h) {
                    // Intersection is top or bottom of rect.
                    h = dy < 0 ? -h : h;
                    return { x: x + (h * dx / dy), y: y + h };
                }
                // Intersection is left or right of rect.
                w = dx < 0 ? -w : w;
                return { x: x + w, y: y + (w * dy / dx) };
            };
            for (const e of g.edges.values()) {
                const edge = e.label;
                const vNode = e.vNode.label;
                const wNode = e.wNode.label;
                let p1;
                let p2;
                if (!edge.points) {
                    edge.points = [];
                    p1 = wNode;
                    p2 = vNode;
                }
                else {
                    p1 = edge.points[0];
                    p2 = edge.points[edge.points.length - 1];
                }
                edge.points.unshift(intersectRect(vNode, p1));
                edge.points.push(intersectRect(wNode, p2));
            }
        };

        time('    makeSpaceForEdgeLabels',        () => makeSpaceForEdgeLabels(g));
        time('    removeSelfEdges',               () => removeSelfEdges(g));
        time('    acyclic_run',                   () => acyclic_run(g));
        time('    nestingGraph_run',              () => nestingGraph_run(g));
        time('    rank',                          () => rank(asNonCompoundGraph(g)));
        time('    injectEdgeLabelProxies',        () => injectEdgeLabelProxies(g));
        time('    removeEmptyRanks',              () => removeEmptyRanks(g));
        time('    nestingGraph_cleanup',          () => nestingGraph_cleanup(g));
        time('    assignRankMinMax',              () => assignRankMinMax(g));
        time('    removeEdgeLabelProxies',        () => removeEdgeLabelProxies(g));
        time('    normalize',                     () => normalize(g));
        time('    parentDummyChains',             () => parentDummyChains(g));
        time('    addBorderSegments',             () => addBorderSegments(g));
        time('    order',                         () => order(g));
        time('    insertSelfEdges',               () => insertSelfEdges(g));
        time('    coordinateSystem_adjust',       () => coordinateSystem_adjust(g));
        time('    position',                      () => position(g));
        time('    positionSelfEdges',             () => positionSelfEdges(g));
        time('    removeBorderNodes',             () => removeBorderNodes(g));
        time('    denormalize',                   () => denormalize(g));
        time('    fixupEdgeLabelCoords',          () => fixupEdgeLabelCoords(g));
        time('    coordinateSystem_undo',         () => coordinateSystem_undo(g));
        time('    translateGraph',                () => translateGraph(g));
        time('    assignNodeIntersects',          () => assignNodeIntersects(g));
        time('    acyclic_undo',                  () => acyclic_undo(g));
    };

    // Copies final layout information from the layout graph back to the input graph.
    // This process only copies whitelisted attributes from the layout graph to the input graph,
    // so it serves as a good place to determine what attributes can influence layout.
    const updateSourceGraph = (graph, g) => {
        for (const node of graph.nodes.values()) {
            const label = node.label;
            if (label) {
                const v = node.v;
                const layoutLabel = g.node(v).label;
                label.x = layoutLabel.x;
                label.y = layoutLabel.y;
                if (g.children(v).length) {
                    label.width = layoutLabel.width;
                    label.height = layoutLabel.height;
                }
            }
        }
        for (const e of graph.edges.values()) {
            const label = g.edge(e.v, e.w).label;
            e.label.points = label.points;
            if ('x' in label) {
                e.label.x = label.x;
                e.label.y = label.y;
            }
        }
        graph.options.width = g.options.width;
        graph.options.height = g.options.height;
    };

    time('layout', () => {
        const layoutGraph =
        time('  buildLayoutGraph',  () => buildLayoutGraph(graph));
        time('  runLayout',         () => runLayout(layoutGraph, time));
        time('  updateSourceGraph', () => updateSourceGraph(graph, layoutGraph));
    });
};

dagre.Graph = class {

    constructor(options) {
        options = options || {};
        this._directed = 'directed' in options ? options.directed : true;
        this._compound = 'compound' in options ? options.compound : false;
        this._label = undefined;
        this._defaultNodeLabelFn = () => {
            return undefined;
        };
        this.nodes = new Map();
        this.edges = new Map();
        if (this._compound) {
            this._parent = {};
            this._children = {};
            this._children['\x00'] = {};
        }
    }

    set options(value) {
        this._label = value;
    }

    get options() {
        return this._label;
    }

    isDirected() {
        return this._directed;
    }

    isCompound() {
        return this._compound;
    }

    setDefaultNodeLabel(newDefault) {
        this._defaultNodeLabelFn = newDefault;
    }

    setNode(v, label) {
        const node = this.nodes.get(v);
        if (node) {
            if (label) {
                node.label = label;
            }
        }
        else {
            const node = { label: label ? label : this._defaultNodeLabelFn(v), in: [], out: [], predecessors: {}, successors: {}, v: v };
            this.nodes.set(v, node);
            if (this._compound) {
                this._parent[v] = '\x00';
                this._children[v] = {};
                this._children['\x00'][v] = true;
            }
        }
    }

    node(v) {
        return this.nodes.get(v);
    }

    hasNode(v) {
        return this.nodes.has(v);
    }

    removeNode(v) {
        const node = this.nodes.get(v);
        if (node) {
            if (this._compound) {
                delete this._children[this._parent[v]][v];
                delete this._parent[v];
                for (const child of this.children(v)) {
                    this.setParent(child);
                }
                delete this._children[v];
            }
            for (const edge of node.in) {
                this.removeEdge(edge);
            }
            for (const edge of node.out) {
                this.removeEdge(edge);
            }
            this.nodes.delete(v);
        }
    }

    setParent(v, parent) {
        if (!this._compound) {
            throw new Error('Cannot set parent in a non-compound graph');
        }
        if (parent) {
            for (let ancestor = parent; ancestor !== undefined; ancestor = this.parent(ancestor)) {
                if (ancestor === v) {
                    throw new Error('Setting ' + parent + ' as parent of ' + v + ' would create a cycle.');
                }
            }
            this.setNode(parent);
        }
        else {
            parent = '\x00';
        }
        delete this._children[this._parent[v]][v];
        this._parent[v] = parent;
        this._children[parent][v] = true;
    }

    parent(v) {
        if (this._compound) {
            const parent = this._parent[v];
            if (parent !== '\x00') {
                return parent;
            }
        }
        return null;
    }

    children(v) {
        if (this._compound) {
            return Object.keys(this._children[v === undefined ? '\x00' : v]);
        }
        else if (v === undefined) {
            return this.nodes.keys();
        }
        else if (this.hasNode(v)) {
            return [];
        }
        return null;
    }

    predecessors(v) {
        return Object.keys(this.nodes.get(v).predecessors);
    }

    successors(v) {
        return Object.keys(this.nodes.get(v).successors);
    }

    neighbors(v) {
        return Array.from(new Set(this.predecessors(v).concat(this.successors(v))));
    }

    edge(v, w) {
        return this.edges.get(this._edgeKey(this._directed, v, w));
    }

    setEdge(v, w, label, name) {
        const key = this._edgeKey(this._directed, v, w, name);
        const edge = this.edges.get(key);
        if (edge) {
            edge.label = label;
        }
        else {
            if (!this._directed && v > w) {
                const tmp = v;
                v = w;
                w = tmp;
            }
            const edge = { label: label, v: v, w: w, name: name, key: key, vNode: null, wNode: null };
            this.edges.set(key, edge);
            this.setNode(v);
            this.setNode(w);
            const wNode = this.nodes.get(w);
            const vNode = this.nodes.get(v);
            edge.wNode = wNode;
            edge.vNode = vNode;
            const incrementOrInitEntry = (map, k) => {
                if (map[k]) {
                    map[k]++;
                }
                else {
                    map[k] = 1;
                }
            };
            incrementOrInitEntry(wNode.predecessors, v);
            incrementOrInitEntry(vNode.successors, w);
            wNode.in.push(edge);
            vNode.out.push(edge);
        }
    }

    removeEdge(edge) {
        const key = edge.key;
        const v = edge.v;
        const w = edge.w;
        const decrementOrRemoveEntry = (map, k) => {
            if (!--map[k]) {
                delete map[k];
            }
        };
        const wNode = edge.wNode;
        const vNode = edge.vNode;
        decrementOrRemoveEntry(wNode.predecessors, v);
        decrementOrRemoveEntry(vNode.successors, w);
        wNode.in = wNode.in.filter((edge) => edge.key !== key);
        vNode.out = vNode.out.filter((edge) => edge.key !== key);
        this.edges.delete(key);
    }

    _edgeKey(isDirected, v, w, name) {
        if (!isDirected && v > w) {
            return name ? w + ':' + v + ':' + name : w + ':' + v + ':';
        }
        return name ? v + ':' + w + ':' + name : v + ':' + w + ':';
    }

    toString() {
        return [
            '[nodes]', Array.from(this.nodes.values()).map(n => JSON.stringify(n.label)).join('\n'),
            '[edges]', Array.from(this.edges.values()).map(e => JSON.stringify(e.label)).join('\n'),
            '[parents]', JSON.stringify(this._parent, null, 2),
            '[children]', JSON.stringify(this._children, null, 2)
        ].join('\n');
    }
};

if (typeof module !== 'undefined' && typeof module.exports === 'object') {
    module.exports = dagre;
}