dc.graph/web/js/dagre.js

Graph visualizations integrated with crossfilter and dc.js

(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.dagre = f()}})(function(){var define,module,exports;return (function(){function r(e,n,t){function o(i,f){if(!n[i]){if(!e[i]){var c="function"==typeof require&&require;if(!f&&c)return c(i,!0);if(u)return u(i,!0);var a=new Error("Cannot find module '"+i+"'");throw a.code="MODULE_NOT_FOUND",a}var p=n[i]={exports:{}};e[i][0].call(p.exports,function(r){var n=e[i][1][r];return o(n||r)},p,p.exports,r,e,n,t)}return n[i].exports}for(var u="function"==typeof require&&require,i=0;i<t.length;i++)o(t[i]);return o}return r})()({1:[function(require,module,exports){
/*
Copyright (c) 2012-2014 Chris Pettitt

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/

module.exports = {
  graphlib: require("./lib/graphlib"),

  layout: require("./lib/layout"),
  debug: require("./lib/debug"),
  util: {
    time: require("./lib/util").time,
    notime: require("./lib/util").notime
  },
  version: require("./lib/version")
};

},{"./lib/debug":6,"./lib/graphlib":7,"./lib/layout":9,"./lib/util":29,"./lib/version":30}],2:[function(require,module,exports){
"use strict";

var _ = require("./lodash");
var greedyFAS = require("./greedy-fas");

module.exports = {
  run: run,
  undo: undo
};

function run(g) {
  var fas = (g.graph().acyclicer === "greedy"
    ? greedyFAS(g, weightFn(g))
    : dfsFAS(g));
  _.forEach(fas, function(e) {
    var label = g.edge(e);
    g.removeEdge(e);
    label.forwardName = e.name;
    label.reversed = true;
    g.setEdge(e.w, e.v, label, _.uniqueId("rev"));
  });

  function weightFn(g) {
    return function(e) {
      return g.edge(e).weight;
    };
  }
}

function dfsFAS(g) {
  var fas = [];
  var stack = {};
  var visited = {};

  function dfs(v) {
    if (_.has(visited, v)) {
      return;
    }
    visited[v] = true;
    stack[v] = true;
    _.forEach(g.outEdges(v), function(e) {
      if (_.has(stack, e.w)) {
        fas.push(e);
      } else {
        dfs(e.w);
      }
    });
    delete stack[v];
  }

  _.forEach(g.nodes(), dfs);
  return fas;
}

function undo(g) {
  _.forEach(g.edges(), function(e) {
    var label = g.edge(e);
    if (label.reversed) {
      g.removeEdge(e);

      var forwardName = label.forwardName;
      delete label.reversed;
      delete label.forwardName;
      g.setEdge(e.w, e.v, label, forwardName);
    }
  });
}

},{"./greedy-fas":8,"./lodash":10}],3:[function(require,module,exports){
var _ = require("./lodash");
var util = require("./util");

module.exports = addBorderSegments;

function addBorderSegments(g) {
  function dfs(v) {
    var children = g.children(v);
    var node = g.node(v);
    if (children.length) {
      _.forEach(children, dfs);
    }

    if (_.has(node, "minRank")) {
      node.borderLeft = [];
      node.borderRight = [];
      for (var rank = node.minRank, maxRank = node.maxRank + 1;
        rank < maxRank;
        ++rank) {
        addBorderNode(g, "borderLeft", "_bl", v, node, rank);
        addBorderNode(g, "borderRight", "_br", v, node, rank);
      }
    }
  }

  _.forEach(g.children(), dfs);
}

function addBorderNode(g, prop, prefix, sg, sgNode, rank) {
  var label = { width: 0, height: 0, rank: rank, borderType: prop };
  var prev = sgNode[prop][rank - 1];
  var curr = util.addDummyNode(g, "border", label, prefix);
  sgNode[prop][rank] = curr;
  g.setParent(curr, sg);
  if (prev) {
    g.setEdge(prev, curr, { weight: 1 });
  }
}

},{"./lodash":10,"./util":29}],4:[function(require,module,exports){
"use strict";

var _ = require("./lodash");

module.exports = {
  adjust: adjust,
  undo: undo
};

function adjust(g) {
  var rankDir = g.graph().rankdir.toLowerCase();
  if (rankDir === "lr" || rankDir === "rl") {
    swapWidthHeight(g);
  }
}

function undo(g) {
  var rankDir = g.graph().rankdir.toLowerCase();
  if (rankDir === "bt" || rankDir === "rl") {
    reverseY(g);
  }

  if (rankDir === "lr" || rankDir === "rl") {
    swapXY(g);
    swapWidthHeight(g);
  }
}

function swapWidthHeight(g) {
  _.forEach(g.nodes(), function(v) { swapWidthHeightOne(g.node(v)); });
  _.forEach(g.edges(), function(e) { swapWidthHeightOne(g.edge(e)); });
}

function swapWidthHeightOne(attrs) {
  var w = attrs.width;
  attrs.width = attrs.height;
  attrs.height = w;
}

function reverseY(g) {
  _.forEach(g.nodes(), function(v) { reverseYOne(g.node(v)); });

  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    _.forEach(edge.points, reverseYOne);
    if (_.has(edge, "y")) {
      reverseYOne(edge);
    }
  });
}

function reverseYOne(attrs) {
  attrs.y = -attrs.y;
}

function swapXY(g) {
  _.forEach(g.nodes(), function(v) { swapXYOne(g.node(v)); });

  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    _.forEach(edge.points, swapXYOne);
    if (_.has(edge, "x")) {
      swapXYOne(edge);
    }
  });
}

function swapXYOne(attrs) {
  var x = attrs.x;
  attrs.x = attrs.y;
  attrs.y = x;
}

},{"./lodash":10}],5:[function(require,module,exports){
/*
 * Simple doubly linked list implementation derived from Cormen, et al.,
 * "Introduction to Algorithms".
 */

module.exports = List;

function List() {
  var sentinel = {};
  sentinel._next = sentinel._prev = sentinel;
  this._sentinel = sentinel;
}

List.prototype.dequeue = function() {
  var sentinel = this._sentinel;
  var entry = sentinel._prev;
  if (entry !== sentinel) {
    unlink(entry);
    return entry;
  }
};

List.prototype.enqueue = function(entry) {
  var sentinel = this._sentinel;
  if (entry._prev && entry._next) {
    unlink(entry);
  }
  entry._next = sentinel._next;
  sentinel._next._prev = entry;
  sentinel._next = entry;
  entry._prev = sentinel;
};

List.prototype.toString = function() {
  var strs = [];
  var sentinel = this._sentinel;
  var curr = sentinel._prev;
  while (curr !== sentinel) {
    strs.push(JSON.stringify(curr, filterOutLinks));
    curr = curr._prev;
  }
  return "[" + strs.join(", ") + "]";
};

function unlink(entry) {
  entry._prev._next = entry._next;
  entry._next._prev = entry._prev;
  delete entry._next;
  delete entry._prev;
}

function filterOutLinks(k, v) {
  if (k !== "_next" && k !== "_prev") {
    return v;
  }
}

},{}],6:[function(require,module,exports){
var _ = require("./lodash");
var util = require("./util");
var Graph = require("./graphlib").Graph;

module.exports = {
  debugOrdering: debugOrdering
};

/* istanbul ignore next */
function debugOrdering(g) {
  var layerMatrix = util.buildLayerMatrix(g);

  var h = new Graph({ compound: true, multigraph: true }).setGraph({});

  _.forEach(g.nodes(), function(v) {
    h.setNode(v, { label: v });
    h.setParent(v, "layer" + g.node(v).rank);
  });

  _.forEach(g.edges(), function(e) {
    h.setEdge(e.v, e.w, {}, e.name);
  });

  _.forEach(layerMatrix, function(layer, i) {
    var layerV = "layer" + i;
    h.setNode(layerV, { rank: "same" });
    _.reduce(layer, function(u, v) {
      h.setEdge(u, v, { style: "invis" });
      return v;
    });
  });

  return h;
}

},{"./graphlib":7,"./lodash":10,"./util":29}],7:[function(require,module,exports){
/* global window */

var graphlib;

if (typeof require === "function") {
  try {
    graphlib = require("graphlib");
  } catch (e) {
    // continue regardless of error
  }
}

if (!graphlib) {
  graphlib = window.graphlib;
}

module.exports = graphlib;

},{"graphlib":31}],8:[function(require,module,exports){
var _ = require("./lodash");
var Graph = require("./graphlib").Graph;
var List = require("./data/list");

/*
 * A greedy heuristic for finding a feedback arc set for a graph. A feedback
 * arc set is a set of edges that can be removed to make a graph acyclic.
 * The algorithm comes from: P. Eades, X. Lin, and W. F. Smyth, "A fast and
 * effective heuristic for the feedback arc set problem." This implementation
 * adjusts that from the paper to allow for weighted edges.
 */
module.exports = greedyFAS;

var DEFAULT_WEIGHT_FN = _.constant(1);

function greedyFAS(g, weightFn) {
  if (g.nodeCount() <= 1) {
    return [];
  }
  var state = buildState(g, weightFn || DEFAULT_WEIGHT_FN);
  var results = doGreedyFAS(state.graph, state.buckets, state.zeroIdx);

  // Expand multi-edges
  return _.flatten(_.map(results, function(e) {
    return g.outEdges(e.v, e.w);
  }), true);
}

function doGreedyFAS(g, buckets, zeroIdx) {
  var results = [];
  var sources = buckets[buckets.length - 1];
  var sinks = buckets[0];

  var entry;
  while (g.nodeCount()) {
    while ((entry = sinks.dequeue()))   { removeNode(g, buckets, zeroIdx, entry); }
    while ((entry = sources.dequeue())) { removeNode(g, buckets, zeroIdx, entry); }
    if (g.nodeCount()) {
      for (var i = buckets.length - 2; i > 0; --i) {
        entry = buckets[i].dequeue();
        if (entry) {
          results = results.concat(removeNode(g, buckets, zeroIdx, entry, true));
          break;
        }
      }
    }
  }

  return results;
}

function removeNode(g, buckets, zeroIdx, entry, collectPredecessors) {
  var results = collectPredecessors ? [] : undefined;

  _.forEach(g.inEdges(entry.v), function(edge) {
    var weight = g.edge(edge);
    var uEntry = g.node(edge.v);

    if (collectPredecessors) {
      results.push({ v: edge.v, w: edge.w });
    }

    uEntry.out -= weight;
    assignBucket(buckets, zeroIdx, uEntry);
  });

  _.forEach(g.outEdges(entry.v), function(edge) {
    var weight = g.edge(edge);
    var w = edge.w;
    var wEntry = g.node(w);
    wEntry["in"] -= weight;
    assignBucket(buckets, zeroIdx, wEntry);
  });

  g.removeNode(entry.v);

  return results;
}

function buildState(g, weightFn) {
  var fasGraph = new Graph();
  var maxIn = 0;
  var maxOut = 0;

  _.forEach(g.nodes(), function(v) {
    fasGraph.setNode(v, { v: v, "in": 0, out: 0 });
  });

  // Aggregate weights on nodes, but also sum the weights across multi-edges
  // into a single edge for the fasGraph.
  _.forEach(g.edges(), function(e) {
    var prevWeight = fasGraph.edge(e.v, e.w) || 0;
    var weight = weightFn(e);
    var edgeWeight = prevWeight + weight;
    fasGraph.setEdge(e.v, e.w, edgeWeight);
    maxOut = Math.max(maxOut, fasGraph.node(e.v).out += weight);
    maxIn  = Math.max(maxIn,  fasGraph.node(e.w)["in"]  += weight);
  });

  var buckets = _.range(maxOut + maxIn + 3).map(function() { return new List(); });
  var zeroIdx = maxIn + 1;

  _.forEach(fasGraph.nodes(), function(v) {
    assignBucket(buckets, zeroIdx, fasGraph.node(v));
  });

  return { graph: fasGraph, buckets: buckets, zeroIdx: zeroIdx };
}

function assignBucket(buckets, zeroIdx, entry) {
  if (!entry.out) {
    buckets[0].enqueue(entry);
  } else if (!entry["in"]) {
    buckets[buckets.length - 1].enqueue(entry);
  } else {
    buckets[entry.out - entry["in"] + zeroIdx].enqueue(entry);
  }
}

},{"./data/list":5,"./graphlib":7,"./lodash":10}],9:[function(require,module,exports){
"use strict";

var _ = require("./lodash");
var acyclic = require("./acyclic");
var normalize = require("./normalize");
var rank = require("./rank");
var normalizeRanks = require("./util").normalizeRanks;
var parentDummyChains = require("./parent-dummy-chains");
var removeEmptyRanks = require("./util").removeEmptyRanks;
var nestingGraph = require("./nesting-graph");
var addBorderSegments = require("./add-border-segments");
var coordinateSystem = require("./coordinate-system");
var order = require("./order");
var position = require("./position");
var util = require("./util");
var Graph = require("./graphlib").Graph;

module.exports = layout;

function layout(g, opts) {
  var time = opts && opts.debugTiming ? util.time : util.notime;
  time("layout", function() {
    var layoutGraph = 
      time("  buildLayoutGraph", function() { return buildLayoutGraph(g); });
    time("  runLayout",        function() { runLayout(layoutGraph, time); });
    time("  updateInputGraph", function() { updateInputGraph(g, layoutGraph); });
  });
}

function runLayout(g, time) {
  time("    makeSpaceForEdgeLabels", function() { makeSpaceForEdgeLabels(g); });
  time("    removeSelfEdges",        function() { removeSelfEdges(g); });
  time("    acyclic",                function() { acyclic.run(g); });
  time("    nestingGraph.run",       function() { nestingGraph.run(g); });
  time("    rank",                   function() { rank(util.asNonCompoundGraph(g)); });
  time("    injectEdgeLabelProxies", function() { injectEdgeLabelProxies(g); });
  time("    removeEmptyRanks",       function() { removeEmptyRanks(g); });
  time("    nestingGraph.cleanup",   function() { nestingGraph.cleanup(g); });
  time("    normalizeRanks",         function() { normalizeRanks(g); });
  time("    assignRankMinMax",       function() { assignRankMinMax(g); });
  time("    removeEdgeLabelProxies", function() { removeEdgeLabelProxies(g); });
  time("    normalize.run",          function() { normalize.run(g); });
  time("    parentDummyChains",      function() { parentDummyChains(g); });
  time("    addBorderSegments",      function() { addBorderSegments(g); });
  time("    order",                  function() { order(g); });
  time("    insertSelfEdges",        function() { insertSelfEdges(g); });
  time("    adjustCoordinateSystem", function() { coordinateSystem.adjust(g); });
  time("    position",               function() { position(g); });
  time("    positionSelfEdges",      function() { positionSelfEdges(g); });
  time("    removeBorderNodes",      function() { removeBorderNodes(g); });
  time("    normalize.undo",         function() { normalize.undo(g); });
  time("    fixupEdgeLabelCoords",   function() { fixupEdgeLabelCoords(g); });
  time("    undoCoordinateSystem",   function() { coordinateSystem.undo(g); });
  time("    translateGraph",         function() { translateGraph(g); });
  time("    assignNodeIntersects",   function() { assignNodeIntersects(g); });
  time("    reversePoints",          function() { reversePointsForReversedEdges(g); });
  time("    acyclic.undo",           function() { 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.
 */
function updateInputGraph(inputGraph, layoutGraph) {
  _.forEach(inputGraph.nodes(), function(v) {
    var inputLabel = inputGraph.node(v);
    var layoutLabel = layoutGraph.node(v);

    if (inputLabel) {
      inputLabel.x = layoutLabel.x;
      inputLabel.y = layoutLabel.y;

      if (layoutGraph.children(v).length) {
        inputLabel.width = layoutLabel.width;
        inputLabel.height = layoutLabel.height;
      }
    }
  });

  _.forEach(inputGraph.edges(), function(e) {
    var inputLabel = inputGraph.edge(e);
    var layoutLabel = layoutGraph.edge(e);

    inputLabel.points = layoutLabel.points;
    if (_.has(layoutLabel, "x")) {
      inputLabel.x = layoutLabel.x;
      inputLabel.y = layoutLabel.y;
    }
  });

  inputGraph.graph().width = layoutGraph.graph().width;
  inputGraph.graph().height = layoutGraph.graph().height;
}

var graphNumAttrs = ["nodesep", "edgesep", "ranksep", "marginx", "marginy"];
var graphDefaults = { ranksep: 50, edgesep: 20, nodesep: 50, rankdir: "tb" };
var graphAttrs = ["acyclicer", "ranker", "rankdir", "align"];
var nodeNumAttrs = ["width", "height"];
var nodeDefaults = { width: 0, height: 0 };
var edgeNumAttrs = ["minlen", "weight", "width", "height", "labeloffset"];
var edgeDefaults = {
  minlen: 1, weight: 1, width: 0, height: 0,
  labeloffset: 10, labelpos: "r"
};
var edgeAttrs = ["labelpos"];

/*
 * 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.
 */
function buildLayoutGraph(inputGraph) {
  var g = new Graph({ multigraph: true, compound: true });
  var graph = canonicalize(inputGraph.graph());

  g.setGraph(_.merge({},
    graphDefaults,
    selectNumberAttrs(graph, graphNumAttrs),
    _.pick(graph, graphAttrs)));

  _.forEach(inputGraph.nodes(), function(v) {
    var node = canonicalize(inputGraph.node(v));
    g.setNode(v, _.defaults(selectNumberAttrs(node, nodeNumAttrs), nodeDefaults));
    g.setParent(v, inputGraph.parent(v));
  });

  _.forEach(inputGraph.edges(), function(e) {
    var edge = canonicalize(inputGraph.edge(e));
    g.setEdge(e, _.merge({},
      edgeDefaults,
      selectNumberAttrs(edge, edgeNumAttrs),
      _.pick(edge, edgeAttrs)));
  });

  return g;
}

/*
 * 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.
 */
function makeSpaceForEdgeLabels(g) {
  var graph = g.graph();
  graph.ranksep /= 2;
  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    edge.minlen *= 2;
    if (edge.labelpos.toLowerCase() !== "c") {
      if (graph.rankdir === "TB" || graph.rankdir === "BT") {
        edge.width += edge.labeloffset;
      } else {
        edge.height += edge.labeloffset;
      }
    }
  });
}

/*
 * 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.
 */
function injectEdgeLabelProxies(g) {
  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    if (edge.width && edge.height) {
      var v = g.node(e.v);
      var w = g.node(e.w);
      var label = { rank: (w.rank - v.rank) / 2 + v.rank, e: e };
      util.addDummyNode(g, "edge-proxy", label, "_ep");
    }
  });
}

function assignRankMinMax(g) {
  var maxRank = 0;
  _.forEach(g.nodes(), function(v) {
    var node = g.node(v);
    if (node.borderTop) {
      node.minRank = g.node(node.borderTop).rank;
      node.maxRank = g.node(node.borderBottom).rank;
      maxRank = _.max(maxRank, node.maxRank);
    }
  });
  g.graph().maxRank = maxRank;
}

function removeEdgeLabelProxies(g) {
  _.forEach(g.nodes(), function(v) {
    var node = g.node(v);
    if (node.dummy === "edge-proxy") {
      g.edge(node.e).labelRank = node.rank;
      g.removeNode(v);
    }
  });
}

function translateGraph(g) {
  var minX = Number.POSITIVE_INFINITY;
  var maxX = 0;
  var minY = Number.POSITIVE_INFINITY;
  var maxY = 0;
  var graphLabel = g.graph();
  var marginX = graphLabel.marginx || 0;
  var marginY = graphLabel.marginy || 0;

  function getExtremes(attrs) {
    var x = attrs.x;
    var y = attrs.y;
    var w = attrs.width;
    var 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);
  }

  _.forEach(g.nodes(), function(v) { getExtremes(g.node(v)); });
  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    if (_.has(edge, "x")) {
      getExtremes(edge);
    }
  });

  minX -= marginX;
  minY -= marginY;

  _.forEach(g.nodes(), function(v) {
    var node = g.node(v);
    node.x -= minX;
    node.y -= minY;
  });

  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    _.forEach(edge.points, function(p) {
      p.x -= minX;
      p.y -= minY;
    });
    if (_.has(edge, "x")) { edge.x -= minX; }
    if (_.has(edge, "y")) { edge.y -= minY; }
  });

  graphLabel.width = maxX - minX + marginX;
  graphLabel.height = maxY - minY + marginY;
}

function assignNodeIntersects(g) {
  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    var nodeV = g.node(e.v);
    var nodeW = g.node(e.w);
    var p1, p2;
    if (!edge.points) {
      edge.points = [];
      p1 = nodeW;
      p2 = nodeV;
    } else {
      p1 = edge.points[0];
      p2 = edge.points[edge.points.length - 1];
    }
    edge.points.unshift(util.intersectRect(nodeV, p1));
    edge.points.push(util.intersectRect(nodeW, p2));
  });
}

function fixupEdgeLabelCoords(g) {
  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    if (_.has(edge, "x")) {
      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;
      }
    }
  });
}

function reversePointsForReversedEdges(g) {
  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    if (edge.reversed) {
      edge.points.reverse();
    }
  });
}

function removeBorderNodes(g) {
  _.forEach(g.nodes(), function(v) {
    if (g.children(v).length) {
      var node = g.node(v);
      var t = g.node(node.borderTop);
      var b = g.node(node.borderBottom);
      var l = g.node(_.last(node.borderLeft));
      var r = g.node(_.last(node.borderRight));

      node.width = Math.abs(r.x - l.x);
      node.height = Math.abs(b.y - t.y);
      node.x = l.x + node.width / 2;
      node.y = t.y + node.height / 2;
    }
  });

  _.forEach(g.nodes(), function(v) {
    if (g.node(v).dummy === "border") {
      g.removeNode(v);
    }
  });
}

function removeSelfEdges(g) {
  _.forEach(g.edges(), function(e) {
    if (e.v === e.w) {
      var node = g.node(e.v);
      if (!node.selfEdges) {
        node.selfEdges = [];
      }
      node.selfEdges.push({ e: e, label: g.edge(e) });
      g.removeEdge(e);
    }
  });
}

function insertSelfEdges(g) {
  var layers = util.buildLayerMatrix(g);
  _.forEach(layers, function(layer) {
    var orderShift = 0;
    _.forEach(layer, function(v, i) {
      var node = g.node(v);
      node.order = i + orderShift;
      _.forEach(node.selfEdges, function(selfEdge) {
        util.addDummyNode(g, "selfedge", {
          width: selfEdge.label.width,
          height: selfEdge.label.height,
          rank: node.rank,
          order: i + (++orderShift),
          e: selfEdge.e,
          label: selfEdge.label
        }, "_se");
      });
      delete node.selfEdges;
    });
  });
}

function positionSelfEdges(g) {
  _.forEach(g.nodes(), function(v) {
    var node = g.node(v);
    if (node.dummy === "selfedge") {
      var selfNode = g.node(node.e.v);
      var x = selfNode.x + selfNode.width / 2;
      var y = selfNode.y;
      var dx = node.x - x;
      var dy = selfNode.height / 2;
      g.setEdge(node.e, node.label);
      g.removeNode(v);
      node.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 }
      ];
      node.label.x = node.x;
      node.label.y = node.y;
    }
  });
}

function selectNumberAttrs(obj, attrs) {
  return _.mapValues(_.pick(obj, attrs), Number);
}

function canonicalize(attrs) {
  var newAttrs = {};
  _.forEach(attrs, function(v, k) {
    newAttrs[k.toLowerCase()] = v;
  });
  return newAttrs;
}

},{"./acyclic":2,"./add-border-segments":3,"./coordinate-system":4,"./graphlib":7,"./lodash":10,"./nesting-graph":11,"./normalize":12,"./order":17,"./parent-dummy-chains":22,"./position":24,"./rank":26,"./util":29}],10:[function(require,module,exports){
/* global window */

var lodash;

if (typeof require === "function") {
  try {
    lodash = {
      cloneDeep: require("lodash/cloneDeep"),
      constant: require("lodash/constant"),
      defaults: require("lodash/defaults"),
      each: require("lodash/each"),
      filter: require("lodash/filter"),
      find: require("lodash/find"),
      flatten: require("lodash/flatten"),
      forEach: require("lodash/forEach"),
      forIn: require("lodash/forIn"),
      has:  require("lodash/has"),
      isUndefined: require("lodash/isUndefined"),
      last: require("lodash/last"),
      map: require("lodash/map"),
      mapValues: require("lodash/mapValues"),
      max: require("lodash/max"),
      merge: require("lodash/merge"),
      min: require("lodash/min"),
      minBy: require("lodash/minBy"),
      now: require("lodash/now"),
      pick: require("lodash/pick"),
      range: require("lodash/range"),
      reduce: require("lodash/reduce"),
      sortBy: require("lodash/sortBy"),
      uniqueId: require("lodash/uniqueId"),
      values: require("lodash/values"),
      zipObject: require("lodash/zipObject"),
    };
  } catch (e) {
    // continue regardless of error
  }
}

if (!lodash) {
  lodash = window._;
}

module.exports = lodash;

},{"lodash/cloneDeep":227,"lodash/constant":228,"lodash/defaults":229,"lodash/each":230,"lodash/filter":232,"lodash/find":233,"lodash/flatten":235,"lodash/forEach":236,"lodash/forIn":237,"lodash/has":239,"lodash/isUndefined":258,"lodash/last":261,"lodash/map":262,"lodash/mapValues":263,"lodash/max":264,"lodash/merge":266,"lodash/min":267,"lodash/minBy":268,"lodash/now":270,"lodash/pick":271,"lodash/range":273,"lodash/reduce":274,"lodash/sortBy":276,"lodash/uniqueId":286,"lodash/values":287,"lodash/zipObject":288}],11:[function(require,module,exports){
var _ = require("./lodash");
var util = require("./util");

module.exports = {
  run: run,
  cleanup: cleanup
};

/*
 * 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 to 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."
 */
function run(g) {
  var root = util.addDummyNode(g, "root", {}, "_root");
  var depths = treeDepths(g);
  var height = _.max(_.values(depths)) - 1; // Note: depths is an Object not an array
  var nodeSep = 2 * height + 1;

  g.graph().nestingRoot = root;

  // Multiply minlen by nodeSep to align nodes on non-border ranks.
  _.forEach(g.edges(), function(e) { g.edge(e).minlen *= nodeSep; });

  // Calculate a weight that is sufficient to keep subgraphs vertically compact
  var weight = sumWeights(g) + 1;

  // Create border nodes and link them up
  _.forEach(g.children(), function(child) {
    dfs(g, root, nodeSep, weight, height, depths, child);
  });

  // Save the multiplier for node layers for later removal of empty border
  // layers.
  g.graph().nodeRankFactor = nodeSep;
}

function dfs(g, root, nodeSep, weight, height, depths, v) {
  var children = g.children(v);
  if (!children.length) {
    if (v !== root) {
      g.setEdge(root, v, { weight: 0, minlen: nodeSep });
    }
    return;
  }

  var top = util.addBorderNode(g, "_bt");
  var bottom = util.addBorderNode(g, "_bb");
  var label = g.node(v);

  g.setParent(top, v);
  label.borderTop = top;
  g.setParent(bottom, v);
  label.borderBottom = bottom;

  _.forEach(children, function(child) {
    dfs(g, root, nodeSep, weight, height, depths, child);

    var childNode = g.node(child);
    var childTop = childNode.borderTop ? childNode.borderTop : child;
    var childBottom = childNode.borderBottom ? childNode.borderBottom : child;
    var thisWeight = childNode.borderTop ? weight : 2 * weight;
    var 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] });
  }
}

function treeDepths(g) {
  var depths = {};
  function dfs(v, depth) {
    var children = g.children(v);
    if (children && children.length) {
      _.forEach(children, function(child) {
        dfs(child, depth + 1);
      });
    }
    depths[v] = depth;
  }
  _.forEach(g.children(), function(v) { dfs(v, 1); });
  return depths;
}

function sumWeights(g) {
  return _.reduce(g.edges(), function(acc, e) {
    return acc + g.edge(e).weight;
  }, 0);
}

function cleanup(g) {
  var graphLabel = g.graph();
  g.removeNode(graphLabel.nestingRoot);
  delete graphLabel.nestingRoot;
  _.forEach(g.edges(), function(e) {
    var edge = g.edge(e);
    if (edge.nestingEdge) {
      g.removeEdge(e);
    }
  });
}

},{"./lodash":10,"./util":29}],12:[function(require,module,exports){
"use strict";

var _ = require("./lodash");
var util = require("./util");

module.exports = {
  run: run,
  undo: undo
};

/*
 * 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.
 */
function run(g) {
  g.graph().dummyChains = [];
  _.forEach(g.edges(), function(edge) { normalizeEdge(g, edge); });
}

function normalizeEdge(g, e) {
  var v = e.v;
  var vRank = g.node(v).rank;
  var w = e.w;
  var wRank = g.node(w).rank;
  var name = e.name;
  var edgeLabel = g.edge(e);
  var labelRank = edgeLabel.labelRank;

  if (wRank === vRank + 1) return;

  g.removeEdge(e);

  var dummy, attrs, i;
  for (i = 0, ++vRank; vRank < wRank; ++i, ++vRank) {
    edgeLabel.points = [];
    attrs = {
      width: 0, height: 0,
      edgeLabel: edgeLabel, edgeObj: e,
      rank: vRank
    };
    dummy = util.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 (i === 0) {
      g.graph().dummyChains.push(dummy);
    }
    v = dummy;
  }

  g.setEdge(v, w, { weight: edgeLabel.weight }, name);
}

function undo(g) {
  _.forEach(g.graph().dummyChains, function(v) {
    var node = g.node(v);
    var origLabel = node.edgeLabel;
    var w;
    g.setEdge(node.edgeObj, origLabel);
    while (node.dummy) {
      w = g.successors(v)[0];
      g.removeNode(v);
      origLabel.points.push({ x: node.x, y: node.y });
      if (node.dummy === "edge-label") {
        origLabel.x = node.x;
        origLabel.y = node.y;
        origLabel.width = node.width;
        origLabel.height = node.height;
      }
      v = w;
      node = g.node(v);
    }
  });
}

},{"./lodash":10,"./util":29}],13:[function(require,module,exports){
var _ = require("../lodash");

module.exports = addSubgraphConstraints;

function addSubgraphConstraints(g, cg, vs) {
  var prev = {},
    rootPrev;

  _.forEach(vs, function(v) {
    var child = g.parent(v),
      parent,
      prevChild;
    while (child) {
      parent = g.parent(child);
      if (parent) {
        prevChild = prev[parent];
        prev[parent] = child;
      } else {
        prevChild = rootPrev;
        rootPrev = child;
      }
      if (prevChild && prevChild !== child) {
        cg.setEdge(prevChild, child);
        return;
      }
      child = parent;
    }
  });

  /*
  function dfs(v) {
    var children = v ? g.children(v) : g.children();
    if (children.length) {
      var min = Number.POSITIVE_INFINITY,
          subgraphs = [];
      _.each(children, function(child) {
        var childMin = dfs(child);
        if (g.children(child).length) {
          subgraphs.push({ v: child, order: childMin });
        }
        min = Math.min(min, childMin);
      });
      _.reduce(_.sortBy(subgraphs, "order"), function(prev, curr) {
        cg.setEdge(prev.v, curr.v);
        return curr;
      });
      return min;
    }
    return g.node(v).order;
  }
  dfs(undefined);
  */
}

},{"../lodash":10}],14:[function(require,module,exports){
var _ = require("../lodash");

module.exports = barycenter;

function barycenter(g, movable) {
  return _.map(movable, function(v) {
    var inV = g.inEdges(v);
    if (!inV.length) {
      return { v: v };
    } else {
      var result = _.reduce(inV, function(acc, e) {
        var edge = g.edge(e),
          nodeU = g.node(e.v);
        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
      };
    }
  });
}


},{"../lodash":10}],15:[function(require,module,exports){
var _ = require("../lodash");
var Graph = require("../graphlib").Graph;

module.exports = buildLayerGraph;

/*
 * 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.
 */
function buildLayerGraph(g, rank, relationship) {
  var root = createRootNode(g),
    result = new Graph({ compound: true }).setGraph({ root: root })
      .setDefaultNodeLabel(function(v) { return g.node(v); });

  _.forEach(g.nodes(), function(v) {
    var node = g.node(v),
      parent = g.parent(v);

    if (node.rank === rank || node.minRank <= rank && rank <= node.maxRank) {
      result.setNode(v);
      result.setParent(v, parent || root);

      // This assumes we have only short edges!
      _.forEach(g[relationship](v), function(e) {
        var u = e.v === v ? e.w : e.v,
          edge = result.edge(u, v),
          weight = !_.isUndefined(edge) ? edge.weight : 0;
        result.setEdge(u, v, { weight: g.edge(e).weight + weight });
      });

      if (_.has(node, "minRank")) {
        result.setNode(v, {
          borderLeft: node.borderLeft[rank],
          borderRight: node.borderRight[rank]
        });
      }
    }
  });

  return result;
}

function createRootNode(g) {
  var v;
  while (g.hasNode((v = _.uniqueId("_root"))));
  return v;
}

},{"../graphlib":7,"../lodash":10}],16:[function(require,module,exports){
"use strict";

var _ = require("../lodash");

module.exports = crossCount;

/*
 * 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."
 */
function crossCount(g, layering) {
  var cc = 0;
  for (var i = 1; i < layering.length; ++i) {
    cc += twoLayerCrossCount(g, layering[i-1], layering[i]);
  }
  return cc;
}

function twoLayerCrossCount(g, northLayer, southLayer) {
  // 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.
  var southPos = _.zipObject(southLayer,
    _.map(southLayer, function (v, i) { return i; }));
  var southEntries = _.flatten(_.map(northLayer, function(v) {
    return _.sortBy(_.map(g.outEdges(v), function(e) {
      return { pos: southPos[e.w], weight: g.edge(e).weight };
    }), "pos");
  }), true);

  // Build the accumulator tree
  var firstIndex = 1;
  while (firstIndex < southLayer.length) firstIndex <<= 1;
  var treeSize = 2 * firstIndex - 1;
  firstIndex -= 1;
  var tree = _.map(new Array(treeSize), function() { return 0; });

  // Calculate the weighted crossings
  var cc = 0;
  _.forEach(southEntries.forEach(function(entry) {
    var index = entry.pos + firstIndex;
    tree[index] += entry.weight;
    var weightSum = 0;
    while (index > 0) {
      if (index % 2) {
        weightSum += tree[index + 1];
      }
      index = (index - 1) >> 1;
      tree[index] += entry.weight;
    }
    cc += entry.weight * weightSum;
  }));

  return cc;
}

},{"../lodash":10}],17:[function(require,module,exports){
"use strict";

var _ = require("../lodash");
var initOrder = require("./init-order");
var crossCount = require("./cross-count");
var sortSubgraph = require("./sort-subgraph");
var buildLayerGraph = require("./build-layer-graph");
var addSubgraphConstraints = require("./add-subgraph-constraints");
var Graph = require("../graphlib").Graph;
var util = require("../util");

module.exports = order;

/*
 * 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 be objects with a "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.
 */
function order(g) {
  var maxRank = util.maxRank(g),
    downLayerGraphs = buildLayerGraphs(g, _.range(1, maxRank + 1), "inEdges"),
    upLayerGraphs = buildLayerGraphs(g, _.range(maxRank - 1, -1, -1), "outEdges");

  var layering = initOrder(g);
  assignOrder(g, layering);

  var bestCC = Number.POSITIVE_INFINITY,
    best;

  for (var i = 0, lastBest = 0; lastBest < 4; ++i, ++lastBest) {
    sweepLayerGraphs(i % 2 ? downLayerGraphs : upLayerGraphs, i % 4 >= 2);

    layering = util.buildLayerMatrix(g);
    var cc = crossCount(g, layering);
    if (cc < bestCC) {
      lastBest = 0;
      best = _.cloneDeep(layering);
      bestCC = cc;
    }
  }

  assignOrder(g, best);
}

function buildLayerGraphs(g, ranks, relationship) {
  return _.map(ranks, function(rank) {
    return buildLayerGraph(g, rank, relationship);
  });
}

function sweepLayerGraphs(layerGraphs, biasRight) {
  var cg = new Graph();
  _.forEach(layerGraphs, function(lg) {
    var root = lg.graph().root;
    var sorted = sortSubgraph(lg, root, cg, biasRight);
    _.forEach(sorted.vs, function(v, i) {
      lg.node(v).order = i;
    });
    addSubgraphConstraints(lg, cg, sorted.vs);
  });
}

function assignOrder(g, layering) {
  _.forEach(layering, function(layer) {
    _.forEach(layer, function(v, i) {
      g.node(v).order = i;
    });
  });
}

},{"../graphlib":7,"../lodash":10,"../util":29,"./add-subgraph-constraints":13,"./build-layer-graph":15,"./cross-count":16,"./init-order":18,"./sort-subgraph":20}],18:[function(require,module,exports){
"use strict";

var _ = require("../lodash");

module.exports = initOrder;

/*
 * 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.
 */
function initOrder(g) {
  var visited = {};
  var simpleNodes = _.filter(g.nodes(), function(v) {
    return !g.children(v).length;
  });
  var maxRank = _.max(_.map(simpleNodes, function(v) { return g.node(v).rank; }));
  var layers = _.map(_.range(maxRank + 1), function() { return []; });

  function dfs(v) {
    if (_.has(visited, v)) return;
    visited[v] = true;
    var node = g.node(v);
    layers[node.rank].push(v);
    _.forEach(g.successors(v), dfs);
  }

  var orderedVs = _.sortBy(simpleNodes, function(v) { return g.node(v).rank; });
  _.forEach(orderedVs, dfs);

  return layers;
}

},{"../lodash":10}],19:[function(require,module,exports){
"use strict";

var _ = require("../lodash");

module.exports = resolveConflicts;

/*
 * 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`.
 */
function resolveConflicts(entries, cg) {
  var mappedEntries = {};
  _.forEach(entries, function(entry, i) {
    var tmp = mappedEntries[entry.v] = {
      indegree: 0,
      "in": [],
      out: [],
      vs: [entry.v],
      i: i
    };
    if (!_.isUndefined(entry.barycenter)) {
      tmp.barycenter = entry.barycenter;
      tmp.weight = entry.weight;
    }
  });

  _.forEach(cg.edges(), function(e) {
    var entryV = mappedEntries[e.v];
    var entryW = mappedEntries[e.w];
    if (!_.isUndefined(entryV) && !_.isUndefined(entryW)) {
      entryW.indegree++;
      entryV.out.push(mappedEntries[e.w]);
    }
  });

  var sourceSet = _.filter(mappedEntries, function(entry) {
    return !entry.indegree;
  });

  return doResolveConflicts(sourceSet);
}

function doResolveConflicts(sourceSet) {
  var entries = [];

  function handleIn(vEntry) {
    return function(uEntry) {
      if (uEntry.merged) {
        return;
      }
      if (_.isUndefined(uEntry.barycenter) ||
          _.isUndefined(vEntry.barycenter) ||
          uEntry.barycenter >= vEntry.barycenter) {
        mergeEntries(vEntry, uEntry);
      }
    };
  }

  function handleOut(vEntry) {
    return function(wEntry) {
      wEntry["in"].push(vEntry);
      if (--wEntry.indegree === 0) {
        sourceSet.push(wEntry);
      }
    };
  }

  while (sourceSet.length) {
    var entry = sourceSet.pop();
    entries.push(entry);
    _.forEach(entry["in"].reverse(), handleIn(entry));
    _.forEach(entry.out, handleOut(entry));
  }

  return _.map(_.filter(entries, function(entry) { return !entry.merged; }),
    function(entry) {
      return _.pick(entry, ["vs", "i", "barycenter", "weight"]);
    });

}

function mergeEntries(target, source) {
  var sum = 0;
  var weight = 0;

  if (target.weight) {
    sum += target.barycenter * target.weight;
    weight += target.weight;
  }

  if (source.weight) {
    sum += source.barycenter * source.weight;
    weight += source.weight;
  }

  target.vs = source.vs.concat(target.vs);
  target.barycenter = sum / weight;
  target.weight = weight;
  target.i = Math.min(source.i, target.i);
  source.merged = true;
}

},{"../lodash":10}],20:[function(require,module,exports){
var _ = require("../lodash");
var barycenter = require("./barycenter");
var resolveConflicts = require("./resolve-conflicts");
var sort = require("./sort");

module.exports = sortSubgraph;

function sortSubgraph(g, v, cg, biasRight) {
  var movable = g.children(v);
  var node = g.node(v);
  var bl = node ? node.borderLeft : undefined;
  var br = node ? node.borderRight: undefined;
  var subgraphs = {};

  if (bl) {
    movable = _.filter(movable, function(w) {
      return w !== bl && w !== br;
    });
  }

  var barycenters = barycenter(g, movable);
  _.forEach(barycenters, function(entry) {
    if (g.children(entry.v).length) {
      var subgraphResult = sortSubgraph(g, entry.v, cg, biasRight);
      subgraphs[entry.v] = subgraphResult;
      if (_.has(subgraphResult, "barycenter")) {
        mergeBarycenters(entry, subgraphResult);
      }
    }
  });

  var entries = resolveConflicts(barycenters, cg);
  expandSubgraphs(entries, subgraphs);

  var result = sort(entries, biasRight);

  if (bl) {
    result.vs = _.flatten([bl, result.vs, br], true);
    if (g.predecessors(bl).length) {
      var blPred = g.node(g.predecessors(bl)[0]),
        brPred = g.node(g.predecessors(br)[0]);
      if (!_.has(result, "barycenter")) {
        result.barycenter = 0;
        result.weight = 0;
      }
      result.barycenter = (result.barycenter * result.weight +
                           blPred.order + brPred.order) / (result.weight + 2);
      result.weight += 2;
    }
  }

  return result;
}

function expandSubgraphs(entries, subgraphs) {
  _.forEach(entries, function(entry) {
    entry.vs = _.flatten(entry.vs.map(function(v) {
      if (subgraphs[v]) {
        return subgraphs[v].vs;
      }
      return v;
    }), true);
  });
}

function mergeBarycenters(target, other) {
  if (!_.isUndefined(target.barycenter)) {
    target.barycenter = (target.barycenter * target.weight +
                         other.barycenter * other.weight) /
                        (target.weight + other.weight);
    target.weight += other.weight;
  } else {
    target.barycenter = other.barycenter;
    target.weight = other.weight;
  }
}

},{"../lodash":10,"./barycenter":14,"./resolve-conflicts":19,"./sort":21}],21:[function(require,module,exports){
var _ = require("../lodash");
var util = require("../util");

module.exports = sort;

function sort(entries, biasRight) {
  var parts = util.partition(entries, function(entry) {
    return _.has(entry, "barycenter");
  });
  var sortable = parts.lhs,
    unsortable = _.sortBy(parts.rhs, function(entry) { return -entry.i; }),
    vs = [],
    sum = 0,
    weight = 0,
    vsIndex = 0;

  sortable.sort(compareWithBias(!!biasRight));

  vsIndex = consumeUnsortable(vs, unsortable, vsIndex);

  _.forEach(sortable, function (entry) {
    vsIndex += entry.vs.length;
    vs.push(entry.vs);
    sum += entry.barycenter * entry.weight;
    weight += entry.weight;
    vsIndex = consumeUnsortable(vs, unsortable, vsIndex);
  });

  var result = { vs: _.flatten(vs, true) };
  if (weight) {
    result.barycenter = sum / weight;
    result.weight = weight;
  }
  return result;
}

function consumeUnsortable(vs, unsortable, index) {
  var last;
  while (unsortable.length && (last = _.last(unsortable)).i <= index) {
    unsortable.pop();
    vs.push(last.vs);
    index++;
  }
  return index;
}

function 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;
  };
}

},{"../lodash":10,"../util":29}],22:[function(require,module,exports){
var _ = require("./lodash");

module.exports = parentDummyChains;

function parentDummyChains(g) {
  var postorderNums = postorder(g);

  _.forEach(g.graph().dummyChains, function(v) {
    var node = g.node(v);
    var edgeObj = node.edgeObj;
    var pathData