homam/index.html

## readme.md

      
    Raw
  

              readme.md
            
          
    This is a sankey diagram used as an example in the book D3 Tips and Tricks. It is based on a simpler version here.
It demonstrates the construction of a sankey diagram using d3.js from external csv data that is formatted using just link data and named values. It should be taken in context with the text of the book which can be downloaded for free from Leanpub.

  
## index.html
<!DOCTYPE html>
<meta charset="utf-8">
<title>SANKEY Experiment</title>
<style>

.node rect {
  cursor: move;
  fill-opacity: .9;
  shape-rendering: crispEdges;
}

.node text {
  pointer-events: none;
  text-shadow: 0 1px 0 #fff;
}

.link {
  fill: none;
  stroke: #000;
  stroke-opacity: .2;
}

.link:hover {
  stroke-opacity: .5;
}

</style>
<body>

<p id="chart">

<script src="http://d3js.org/d3.v3.min.js"></script>
<script src="sankey.js"></script>
<script>

var units = "Widgets";

var margin = {top: 10, right: 10, bottom: 10, left: 10},
    width = 700 - margin.left - margin.right,
    height = 300 - margin.top - margin.bottom;

var formatNumber = d3.format(",.0f"),    // zero decimal places
    format = function(d) { return formatNumber(d) + " " + units; },
    color = d3.scale.category20();

// append the svg canvas to the page
var svg = d3.select("#chart").append("svg")
    .attr("width", width + margin.left + margin.right)
    .attr("height", height + margin.top + margin.bottom)
  .append("g")
    .attr("transform",
          "translate(" + margin.left + "," + margin.top + ")");

// Set the sankey diagram properties
var sankey = d3.sankey()
    .nodeWidth(36)
    .nodePadding(40)
    .size([width, height]);

var path = sankey.link();

// load the data (using the timelyportfolio csv method)
d3.csv("sankey.csv?rnd=" + Math.random(), function(error, data) {

  //set up graph in same style as original example but empty
  graph = {"nodes" : [], "links" : []};

    data.forEach(function (d) {
      graph.nodes.push({ "name": d.source });
      graph.nodes.push({ "name": d.target });
      graph.links.push({ "source": d.source,
                         "target": d.target,
                         "value": +d.value });
     });

     // return only the distinct / unique nodes
     graph.nodes = d3.keys(d3.nest()
       .key(function (d) { return d.name; })
       .map(graph.nodes));

     // loop through each link replacing the text with its index from node
     graph.links.forEach(function (d, i) {
       graph.links[i].source = graph.nodes.indexOf(graph.links[i].source);
       graph.links[i].target = graph.nodes.indexOf(graph.links[i].target);
     });

     //now loop through each nodes to make nodes an array of objects
     // rather than an array of strings
     graph.nodes.forEach(function (d, i) {
       graph.nodes[i] = { "name": d };
     });

  sankey
    .nodes(graph.nodes)
    .links(graph.links)
    .layout(32);

// add in the links
  var link = svg.append("g").selectAll(".link")
      .data(graph.links)
    .enter().append("path")
      .attr("class", "link")
      .attr("d", path)
      .style("stroke-width", function(d) { return Math.max(1, d.dy); })
      .sort(function(a, b) { return b.dy - a.dy; });

// add the link titles
  link.append("title")
        .text(function(d) {
    		return d.source.name + " → " +
                d.target.name + "\n" + format(d.value); });

// add in the nodes
  var node = svg.append("g").selectAll(".node")
      .data(graph.nodes)
    .enter().append("g")
      .attr("class", "node")
      .attr("transform", function(d) {
		  return "translate(" + d.x + "," + d.y + ")"; })
    .call(d3.behavior.drag()
      .origin(function(d) { return d; })
      .on("dragstart", function() {
		  this.parentNode.appendChild(this); })
      .on("drag", dragmove));

// add the rectangles for the nodes
  node.append("rect")
      .attr("height", function(d) { return d.dy; })
      .attr("width", sankey.nodeWidth())
      .style("fill", function(d) {
		  return d.color = color(d.name.replace(/ .*/, "")); })
      .style("stroke", function(d) {
		  return d3.rgb(d.color).darker(2); })
    .append("title")
      .text(function(d) {
		  return d.name + "\n" + format(d.value); });

// add in the title for the nodes
  node.append("text")
      .attr("x", -6)
      .attr("y", function(d) { return d.dy / 2; })
      .attr("dy", ".35em")
      .attr("text-anchor", "end")
      .attr("transform", null)
      .text(function(d) { return d.name; })
    .filter(function(d) { return d.x < width / 2; })
      .attr("x", 6 + sankey.nodeWidth())
      .attr("text-anchor", "start");

// the function for moving the nodes
  function dragmove(d) {
    d3.select(this).attr("transform",
        "translate(" + d.x + "," + (
                d.y = Math.max(0, Math.min(height - d.dy, d3.event.y))
            ) + ")");
    sankey.relayout();
    link.attr("d", path);
  }
});

</script>

</body>
</html>

## sankey.csv

          
            source
            target
            value
            row
            web
            next_web
            next_retail
            count

            
              1_web
              2_web
              35
              1
              1
              1
              0
              35

            
              1_web
              2_retail
              105
              1
              1
              0
              1
              105

            
              1_retail
              2_retail
              193
              1
              0
              0
              1
              193

            
              1_retail
              2_web
              92
              1
              0
              1
              0
              92

            
              1_retail
              2_out
              680
              1
              0
              
              
              680

            
              1_web
              2_out
              83
              1
              1
              
              
              83

            
              2_web
              3_retail
              44
              2
              1
              0
              1
              44

            
              2_retail
              3_web
              44
              2
              0
              1
              0
              44

            
              2_web
              3_web
              21
              2
              1
              1
              0
              21

            
              2_web
              3_out
              62
              2
              1
              
              
              62

            
              2_retail
              3_out
              178
              2
              0
              
              
              178

            
              2_retail
              3_retail
              76
              2
              0
              0
              1
              76

            
              3_web
              4_web
              13
              3
              1
              1
              0
              13

            
              3_retail
              4_out
              74
              3
              0
              
              
              74

            
              3_retail
              4_retail
              36
              3
              0
              0
              1
              36

            
              3_web
              4_out
              33
              3
              1
              
              
              33

            
              3_retail
              4_web
              10
              3
              0
              1
              0
              10

            
              3_web
              4_retail
              19
              3
              1
              0
              1
              19

            
              4_web
              5_web
              4
              4
              1
              1
              0
              4

            
              4_retail
              5_retail
              23
              4
              0
              0
              1
              23

            
              4_retail
              5_out
              26
              4
              0
              
              
              26

            
              4_retail
              5_web
              6
              4
              0
              1
              0
              6

            
              4_web
              5_out
              9
              4
              1
              
              
              9

            
              4_web
              5_retail
              10
              4
              1
              0
              1
              10

            
              5_web
              6_web
              3
              5
              1
              1
              0
              3

            
              5_retail
              6_out
              17
              5
              0
              
              
              17

            
              5_web
              6_out
              3
              5
              1
              
              
              3

            
              5_retail
              6_web
              7
              5
              0
              1
              0
              7

            
              5_web
              6_retail
              4
              5
              1
              0
              1
              4

            
              5_retail
              6_retail
              9
              5
              0
              0
              1
              9

## sankey.js
d3.sankey = function() {
  var sankey = {},
      nodeWidth = 24,
      nodePadding = 8,
      size = [1, 1],
      nodes = [],
      links = [];

  sankey.nodeWidth = function(_) {
    if (!arguments.length) return nodeWidth;
    nodeWidth = +_;
    return sankey;
  };

  sankey.nodePadding = function(_) {
    if (!arguments.length) return nodePadding;
    nodePadding = +_;
    return sankey;
  };

  sankey.nodes = function(_) {
    if (!arguments.length) return nodes;
    nodes = _;
    return sankey;
  };

  sankey.links = function(_) {
    if (!arguments.length) return links;
    links = _;
    return sankey;
  };

  sankey.size = function(_) {
    if (!arguments.length) return size;
    size = _;
    return sankey;
  };

  sankey.layout = function(iterations) {
    computeNodeLinks();
    computeNodeValues();
    computeNodeBreadths();
    computeNodeDepths(iterations);
    computeLinkDepths();
    return sankey;
  };

  sankey.relayout = function() {
    computeLinkDepths();
    return sankey;
  };

  sankey.link = function() {
    var curvature = .5;

    function link(d) {
      var x0 = d.source.x + d.source.dx,
          x1 = d.target.x,
          xi = d3.interpolateNumber(x0, x1),
          x2 = xi(curvature),
          x3 = xi(1 - curvature),
          y0 = d.source.y + d.sy + d.dy / 2,
          y1 = d.target.y + d.ty + d.dy / 2;
      return "M" + x0 + "," + y0
           + "C" + x2 + "," + y0
           + " " + x3 + "," + y1
           + " " + x1 + "," + y1;
    }

    link.curvature = function(_) {
      if (!arguments.length) return curvature;
      curvature = +_;
      return link;
    };

    return link;
  };

  // Populate the sourceLinks and targetLinks for each node.
  // Also, if the source and target are not objects, assume they are indices.
  function computeNodeLinks() {
    nodes.forEach(function(node) {
      node.sourceLinks = [];
      node.targetLinks = [];
    });
    links.forEach(function(link) {
      var source = link.source,
          target = link.target;
      if (typeof source === "number") source = link.source = nodes[link.source];
      if (typeof target === "number") target = link.target = nodes[link.target];
      source.sourceLinks.push(link);
      target.targetLinks.push(link);
    });
  }

  // Compute the value (size) of each node by summing the associated links.
  function computeNodeValues() {
    nodes.forEach(function(node) {
      node.value = Math.max(
        d3.sum(node.sourceLinks, value),
        d3.sum(node.targetLinks, value)
      );
    });
  }

  // Iteratively assign the breadth (x-position) for each node.
  // Nodes are assigned the maximum breadth of incoming neighbors plus one;
  // nodes with no incoming links are assigned breadth zero, while
  // nodes with no outgoing links are assigned the maximum breadth.
  function computeNodeBreadths() {
    var remainingNodes = nodes,
        nextNodes,
        x = 0;

    while (remainingNodes.length) {
      nextNodes = [];
      remainingNodes.forEach(function(node) {
        node.x = x;
        node.dx = nodeWidth;
        node.sourceLinks.forEach(function(link) {
          nextNodes.push(link.target);
        });
      });
      remainingNodes = nextNodes;
      ++x;
    }

    //
    moveSinksRight(x);
    scaleNodeBreadths((width - nodeWidth) / (x - 1));
  }

  function moveSourcesRight() {
    nodes.forEach(function(node) {
      if (!node.targetLinks.length) {
        node.x = d3.min(node.sourceLinks, function(d) { return d.target.x; }) - 1;
      }
    });
  }

  function moveSinksRight(x) {
    nodes.forEach(function(node) {
      if (!node.sourceLinks.length) {
        node.x = x - 1;
      }
    });
  }

  function scaleNodeBreadths(kx) {
    nodes.forEach(function(node) {
      node.x *= kx;
    });
  }

  function computeNodeDepths(iterations) {
    var nodesByBreadth = d3.nest()
        .key(function(d) { return d.x; })
        .sortKeys(d3.ascending)
        .entries(nodes)
        .map(function(d) { return d.values; });

    //
    initializeNodeDepth();
    resolveCollisions();
    for (var alpha = 1; iterations > 0; --iterations) {
      relaxRightToLeft(alpha *= .99);
      resolveCollisions();
      relaxLeftToRight(alpha);
      resolveCollisions();
    }

    function initializeNodeDepth() {
      var ky = d3.min(nodesByBreadth, function(nodes) {
        return (size[1] - (nodes.length - 1) * nodePadding) / d3.sum(nodes, value);
      });

      nodesByBreadth.forEach(function(nodes) {
        nodes.forEach(function(node, i) {
          node.y = i;
          node.dy = node.value * ky;
        });
      });

      links.forEach(function(link) {
        link.dy = link.value * ky;
      });
    }

    function relaxLeftToRight(alpha) {
      nodesByBreadth.forEach(function(nodes, breadth) {
        nodes.forEach(function(node) {
          if (node.targetLinks.length) {
            var y = d3.sum(node.targetLinks, weightedSource) / d3.sum(node.targetLinks, value);
            node.y += (y - center(node)) * alpha;
          }
        });
      });

      function weightedSource(link) {
        return center(link.source) * link.value;
      }
    }

    function relaxRightToLeft(alpha) {
      nodesByBreadth.slice().reverse().forEach(function(nodes) {
        nodes.forEach(function(node) {
          if (node.sourceLinks.length) {
            var y = d3.sum(node.sourceLinks, weightedTarget) / d3.sum(node.sourceLinks, value);
            node.y += (y - center(node)) * alpha;
          }
        });
      });

      function weightedTarget(link) {
        return center(link.target) * link.value;
      }
    }

    function resolveCollisions() {
      nodesByBreadth.forEach(function(nodes) {
        var node,
            dy,
            y0 = 0,
            n = nodes.length,
            i;

        // Push any overlapping nodes down.
        nodes.sort(ascendingDepth);
        for (i = 0; i < n; ++i) {
          node = nodes[i];
          dy = y0 - node.y;
          if (dy > 0) node.y += dy;
          y0 = node.y + node.dy + nodePadding;
        }

        // If the bottommost node goes outside the bounds, push it back up.
        dy = y0 - nodePadding - size[1];
        if (dy > 0) {
          y0 = node.y -= dy;

          // Push any overlapping nodes back up.
          for (i = n - 2; i >= 0; --i) {
            node = nodes[i];
            dy = node.y + node.dy + nodePadding - y0;
            if (dy > 0) node.y -= dy;
            y0 = node.y;
          }
        }
      });
    }

    function ascendingDepth(a, b) {
      return a.y - b.y;
    }
  }

  function computeLinkDepths() {
    nodes.forEach(function(node) {
      node.sourceLinks.sort(ascendingTargetDepth);
      node.targetLinks.sort(ascendingSourceDepth);
    });
    nodes.forEach(function(node) {
      var sy = 0, ty = 0;
      node.sourceLinks.forEach(function(link) {
        link.sy = sy;
        sy += link.dy;
      });
      node.targetLinks.forEach(function(link) {
        link.ty = ty;
        ty += link.dy;
      });
    });

    function ascendingSourceDepth(a, b) {
      return a.source.y - b.source.y;
    }

    function ascendingTargetDepth(a, b) {
      return a.target.y - b.target.y;
    }
  }

  function center(node) {
    return node.y + node.dy / 2;
  }

  function value(link) {
    return link.value;
  }

  return sankey;
};

## thumbnail.png

      
    Raw
  

              thumbnail.png
	<!DOCTYPE html>
	<meta charset="utf-8">
	<title>SANKEY Experiment</title>
	<style>

	.node rect {
	cursor: move;
	fill-opacity: .9;
	shape-rendering: crispEdges;
	}

	.node text {
	pointer-events: none;
	text-shadow: 0 1px 0 #fff;
	}

	.link {
	fill: none;
	stroke: #000;
	stroke-opacity: .2;
	}

	.link:hover {
	stroke-opacity: .5;
	}

	</style>
	<body>

	<p id="chart">

	<script src="http://d3js.org/d3.v3.min.js"></script>
	<script src="sankey.js"></script>
	<script>

	var units = "Widgets";

	var margin = {top: 10, right: 10, bottom: 10, left: 10},
	width = 700 - margin.left - margin.right,
	height = 300 - margin.top - margin.bottom;

	var formatNumber = d3.format(",.0f"), // zero decimal places
	format = function(d) { return formatNumber(d) + " " + units; },
	color = d3.scale.category20();

	// append the svg canvas to the page
	var svg = d3.select("#chart").append("svg")
	.attr("width", width + margin.left + margin.right)
	.attr("height", height + margin.top + margin.bottom)
	.append("g")
	.attr("transform",
	"translate(" + margin.left + "," + margin.top + ")");

	// Set the sankey diagram properties
	var sankey = d3.sankey()
	.nodeWidth(36)
	.nodePadding(40)
	.size([width, height]);

	var path = sankey.link();

	// load the data (using the timelyportfolio csv method)
	d3.csv("sankey.csv?rnd=" + Math.random(), function(error, data) {

	//set up graph in same style as original example but empty
	graph = {"nodes" : [], "links" : []};

	data.forEach(function (d) {
	graph.nodes.push({ "name": d.source });
	graph.nodes.push({ "name": d.target });
	graph.links.push({ "source": d.source,
	"target": d.target,
	"value": +d.value });
	});

	// return only the distinct / unique nodes
	graph.nodes = d3.keys(d3.nest()
	.key(function (d) { return d.name; })
	.map(graph.nodes));

	// loop through each link replacing the text with its index from node
	graph.links.forEach(function (d, i) {
	graph.links[i].source = graph.nodes.indexOf(graph.links[i].source);
	graph.links[i].target = graph.nodes.indexOf(graph.links[i].target);
	});

	//now loop through each nodes to make nodes an array of objects
	// rather than an array of strings
	graph.nodes.forEach(function (d, i) {
	graph.nodes[i] = { "name": d };
	});

	sankey
	.nodes(graph.nodes)
	.links(graph.links)
	.layout(32);

	// add in the links
	var link = svg.append("g").selectAll(".link")
	.data(graph.links)
	.enter().append("path")
	.attr("class", "link")
	.attr("d", path)
	.style("stroke-width", function(d) { return Math.max(1, d.dy); })
	.sort(function(a, b) { return b.dy - a.dy; });

	// add the link titles
	link.append("title")
	.text(function(d) {
	return d.source.name + " → " +
	d.target.name + "\n" + format(d.value); });

	// add in the nodes
	var node = svg.append("g").selectAll(".node")
	.data(graph.nodes)
	.enter().append("g")
	.attr("class", "node")
	.attr("transform", function(d) {
	return "translate(" + d.x + "," + d.y + ")"; })
	.call(d3.behavior.drag()
	.origin(function(d) { return d; })
	.on("dragstart", function() {
	this.parentNode.appendChild(this); })
	.on("drag", dragmove));

	// add the rectangles for the nodes
	node.append("rect")
	.attr("height", function(d) { return d.dy; })
	.attr("width", sankey.nodeWidth())
	.style("fill", function(d) {
	return d.color = color(d.name.replace(/ .*/, "")); })
	.style("stroke", function(d) {
	return d3.rgb(d.color).darker(2); })
	.append("title")
	.text(function(d) {
	return d.name + "\n" + format(d.value); });

	// add in the title for the nodes
	node.append("text")
	.attr("x", -6)
	.attr("y", function(d) { return d.dy / 2; })
	.attr("dy", ".35em")
	.attr("text-anchor", "end")
	.attr("transform", null)
	.text(function(d) { return d.name; })
	.filter(function(d) { return d.x < width / 2; })
	.attr("x", 6 + sankey.nodeWidth())
	.attr("text-anchor", "start");

	// the function for moving the nodes
	function dragmove(d) {
	d3.select(this).attr("transform",
	"translate(" + d.x + "," + (
	d.y = Math.max(0, Math.min(height - d.dy, d3.event.y))
	) + ")");
	sankey.relayout();
	link.attr("d", path);
	}
	});

	</script>

	</body>
	</html>
source	target	value	row	web	next_web	next_retail	count
1_web	2_web	35	1	1	1	0	35
1_web	2_retail	105	1	1	0	1	105
1_retail	2_retail	193	1	0	0	1	193
1_retail	2_web	92	1	0	1	0	92
1_retail	2_out	680	1	0			680
1_web	2_out	83	1	1			83
2_web	3_retail	44	2	1	0	1	44
2_retail	3_web	44	2	0	1	0	44
2_web	3_web	21	2	1	1	0	21
2_web	3_out	62	2	1			62
2_retail	3_out	178	2	0			178
2_retail	3_retail	76	2	0	0	1	76
3_web	4_web	13	3	1	1	0	13
3_retail	4_out	74	3	0			74
3_retail	4_retail	36	3	0	0	1	36
3_web	4_out	33	3	1			33
3_retail	4_web	10	3	0	1	0	10
3_web	4_retail	19	3	1	0	1	19
4_web	5_web	4	4	1	1	0	4
4_retail	5_retail	23	4	0	0	1	23
4_retail	5_out	26	4	0			26
4_retail	5_web	6	4	0	1	0	6
4_web	5_out	9	4	1			9
4_web	5_retail	10	4	1	0	1	10
5_web	6_web	3	5	1	1	0	3
5_retail	6_out	17	5	0			17
5_web	6_out	3	5	1			3
5_retail	6_web	7	5	0	1	0	7
5_web	6_retail	4	5	1	0	1	4
5_retail	6_retail	9	5	0	0	1	9
	d3.sankey = function() {
	var sankey = {},
	nodeWidth = 24,
	nodePadding = 8,
	size = [1, 1],
	nodes = [],
	links = [];

	sankey.nodeWidth = function(_) {
	if (!arguments.length) return nodeWidth;
	nodeWidth = +_;
	return sankey;
	};

	sankey.nodePadding = function(_) {
	if (!arguments.length) return nodePadding;
	nodePadding = +_;
	return sankey;
	};

	sankey.nodes = function(_) {
	if (!arguments.length) return nodes;
	nodes = _;
	return sankey;
	};

	sankey.links = function(_) {
	if (!arguments.length) return links;
	links = _;
	return sankey;
	};

	sankey.size = function(_) {
	if (!arguments.length) return size;
	size = _;
	return sankey;
	};

	sankey.layout = function(iterations) {
	computeNodeLinks();
	computeNodeValues();
	computeNodeBreadths();
	computeNodeDepths(iterations);
	computeLinkDepths();
	return sankey;
	};

	sankey.relayout = function() {
	computeLinkDepths();
	return sankey;
	};

	sankey.link = function() {
	var curvature = .5;

	function link(d) {
	var x0 = d.source.x + d.source.dx,
	x1 = d.target.x,
	xi = d3.interpolateNumber(x0, x1),
	x2 = xi(curvature),
	x3 = xi(1 - curvature),
	y0 = d.source.y + d.sy + d.dy / 2,
	y1 = d.target.y + d.ty + d.dy / 2;
	return "M" + x0 + "," + y0
	+ "C" + x2 + "," + y0
	+ " " + x3 + "," + y1
	+ " " + x1 + "," + y1;
	}

	link.curvature = function(_) {
	if (!arguments.length) return curvature;
	curvature = +_;
	return link;
	};

	return link;
	};

	// Populate the sourceLinks and targetLinks for each node.
	// Also, if the source and target are not objects, assume they are indices.
	function computeNodeLinks() {
	nodes.forEach(function(node) {
	node.sourceLinks = [];
	node.targetLinks = [];
	});
	links.forEach(function(link) {
	var source = link.source,
	target = link.target;
	if (typeof source === "number") source = link.source = nodes[link.source];
	if (typeof target === "number") target = link.target = nodes[link.target];
	source.sourceLinks.push(link);
	target.targetLinks.push(link);
	});
	}

	// Compute the value (size) of each node by summing the associated links.
	function computeNodeValues() {
	nodes.forEach(function(node) {
	node.value = Math.max(
	d3.sum(node.sourceLinks, value),
	d3.sum(node.targetLinks, value)
	);
	});
	}

	// Iteratively assign the breadth (x-position) for each node.
	// Nodes are assigned the maximum breadth of incoming neighbors plus one;
	// nodes with no incoming links are assigned breadth zero, while
	// nodes with no outgoing links are assigned the maximum breadth.
	function computeNodeBreadths() {
	var remainingNodes = nodes,
	nextNodes,
	x = 0;

	while (remainingNodes.length) {
	nextNodes = [];
	remainingNodes.forEach(function(node) {
	node.x = x;
	node.dx = nodeWidth;
	node.sourceLinks.forEach(function(link) {
	nextNodes.push(link.target);
	});
	});
	remainingNodes = nextNodes;
	++x;
	}

	//
	moveSinksRight(x);
	scaleNodeBreadths((width - nodeWidth) / (x - 1));
	}

	function moveSourcesRight() {
	nodes.forEach(function(node) {
	if (!node.targetLinks.length) {
	node.x = d3.min(node.sourceLinks, function(d) { return d.target.x; }) - 1;
	}
	});
	}

	function moveSinksRight(x) {
	nodes.forEach(function(node) {
	if (!node.sourceLinks.length) {
	node.x = x - 1;
	}
	});
	}

	function scaleNodeBreadths(kx) {
	nodes.forEach(function(node) {
	node.x *= kx;
	});
	}

	function computeNodeDepths(iterations) {
	var nodesByBreadth = d3.nest()
	.key(function(d) { return d.x; })
	.sortKeys(d3.ascending)
	.entries(nodes)
	.map(function(d) { return d.values; });

	//
	initializeNodeDepth();
	resolveCollisions();
	for (var alpha = 1; iterations > 0; --iterations) {
	relaxRightToLeft(alpha *= .99);
	resolveCollisions();
	relaxLeftToRight(alpha);
	resolveCollisions();
	}

	function initializeNodeDepth() {
	var ky = d3.min(nodesByBreadth, function(nodes) {
	return (size[1] - (nodes.length - 1) * nodePadding) / d3.sum(nodes, value);
	});

	nodesByBreadth.forEach(function(nodes) {
	nodes.forEach(function(node, i) {
	node.y = i;
	node.dy = node.value * ky;
	});
	});

	links.forEach(function(link) {
	link.dy = link.value * ky;
	});
	}

	function relaxLeftToRight(alpha) {
	nodesByBreadth.forEach(function(nodes, breadth) {
	nodes.forEach(function(node) {
	if (node.targetLinks.length) {
	var y = d3.sum(node.targetLinks, weightedSource) / d3.sum(node.targetLinks, value);
	node.y += (y - center(node)) * alpha;
	}
	});
	});

	function weightedSource(link) {
	return center(link.source) * link.value;
	}
	}

	function relaxRightToLeft(alpha) {
	nodesByBreadth.slice().reverse().forEach(function(nodes) {
	nodes.forEach(function(node) {
	if (node.sourceLinks.length) {
	var y = d3.sum(node.sourceLinks, weightedTarget) / d3.sum(node.sourceLinks, value);
	node.y += (y - center(node)) * alpha;
	}
	});
	});

	function weightedTarget(link) {
	return center(link.target) * link.value;
	}
	}

	function resolveCollisions() {
	nodesByBreadth.forEach(function(nodes) {
	var node,
	dy,
	y0 = 0,
	n = nodes.length,
	i;

	// Push any overlapping nodes down.
	nodes.sort(ascendingDepth);
	for (i = 0; i < n; ++i) {
	node = nodes[i];
	dy = y0 - node.y;
	if (dy > 0) node.y += dy;
	y0 = node.y + node.dy + nodePadding;
	}

	// If the bottommost node goes outside the bounds, push it back up.
	dy = y0 - nodePadding - size[1];
	if (dy > 0) {
	y0 = node.y -= dy;

	// Push any overlapping nodes back up.
	for (i = n - 2; i >= 0; --i) {
	node = nodes[i];
	dy = node.y + node.dy + nodePadding - y0;
	if (dy > 0) node.y -= dy;
	y0 = node.y;
	}
	}
	});
	}

	function ascendingDepth(a, b) {
	return a.y - b.y;
	}
	}

	function computeLinkDepths() {
	nodes.forEach(function(node) {
	node.sourceLinks.sort(ascendingTargetDepth);
	node.targetLinks.sort(ascendingSourceDepth);
	});
	nodes.forEach(function(node) {
	var sy = 0, ty = 0;
	node.sourceLinks.forEach(function(link) {
	link.sy = sy;
	sy += link.dy;
	});
	node.targetLinks.forEach(function(link) {
	link.ty = ty;
	ty += link.dy;
	});
	});

	function ascendingSourceDepth(a, b) {
	return a.source.y - b.source.y;
	}

	function ascendingTargetDepth(a, b) {
	return a.target.y - b.target.y;
	}
	}

	function center(node) {
	return node.y + node.dy / 2;
	}

	function value(link) {
	return link.value;
	}

	return sankey;
	};