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sankey
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index.html
<!DOCTYPE html>
<html>
<meta charset="utf-8">
<title>Sankey Diagram</title>
<style>
@import url(style.css);
#chart {
height: 500px;
}
.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>
<header>
<aside>May 22, 2012</aside>
<a href="../" rel="author">Mike Bostock</a>
</header>
<h1>Sankey Diagrams</h1>
<p id="chart">
<aside>Drag to rearrange nodes.</aside>
<p class="attribution">Source: <a href="http://www.decc.gov.uk/en/content/cms/tackling/2050/calculator_on/calculator_on.aspx">Department of Energy & Climate Change</a>, <a href="http://tamc.github.com/Sankey/">Tom Counsell</a>.
<aside>Sankey diagrams are closely related to <a href="http://en.wikipedia.org/wiki/Alluvial_diagram">alluvial diagrams</a>, which show how network structure changes over time.</aside>
<p><a href="http://en.wikipedia.org/wiki/Sankey_diagram">Sankey diagrams</a> visualize the magnitude of flow between nodes in a network. This intricate diagram shows a possible scenario for UK energy production and consumption in 2050: energy <b>supplies</b> are on the left, and <b>demands</b> are on the right. Intermediate nodes group related forms of production and show how energy is converted and transmitted before it is consumed (or lost!). The thickness of each link encodes the amount of flow from source to target.
<p>This example is built with <a href="http://d3js.org">D3</a>’s <a href="https://github.com/d3/d3-plugins/tree/master/sankey">Sankey plugin</a>. The plugin takes as input the nodes and weighted links, computing positions via <a href="http://en.wikipedia.org/wiki/Gauss–Seidel_method">iterative relaxation</a>. After fixing the horizontal position of each node, the algorithm starts from the sources on the left, positioning downstream nodes so as to minimize link distance. A reverse pass is then made from right-to-left, and then the entire process is repeated several times. Overlapping nodes are shifted to avoid collision.
<aside>The d3.sankey API is similar to D3’s <a href="http://mbostock.github.com/d3/ex/force.html">force-directed graph</a> layout, which is another type of network visualization.</aside>
<p>The fully automatic layout is convenient for rapid visualization—positioning nodes manually is tedious! However, the algorithm is not perfect; links are drawn with partial transparency to highlight crossings. To improve readability and further disambiguate links, this example also lets you reposition nodes interactively. The algorithm could be improved in the future, say to minimize link crossing or to support loopback in cyclical networks.
<p>Many thanks to Tom Counsell, whose <a href="http://tamc.github.com/Sankey/">Sankey library</a> provided inspiration for this example.
<footer>
<aside>May 22, 2012</aside>
<a href="../" rel="author">Mike Bostock</a>
</footer>
<script src="http://d3js.org/d3.v2.min.js?2.9.1"></script>
<script src="sankey.js"></script>
<script>
var margin = {top: 1, right: 1, bottom: 6, left: 1},
width = 960 - margin.left - margin.right,
height = 500 - margin.top - margin.bottom;
var formatNumber = d3.format(",.0f"),
format = function(d) { return formatNumber(d) + " TWh"; },
color = d3.scale.category20();
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 + ")");
var sankey = d3.sankey()
.nodeWidth(15)
.nodePadding(10)
.size([width, height]);
var path = sankey.link();
d3.json("energy.json", function(energy) {
sankey
.nodes(energy.nodes)
.links(energy.links)
.layout(32);
var link = svg.append("g").selectAll(".link")
.data(energy.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; });
link.append("title")
.text(function(d) { return d.source.name + " → " + d.target.name + "\n" + format(d.value); });
var node = svg.append("g").selectAll(".node")
.data(energy.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));
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); });
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");
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>
Raw
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;
};
Raw
style.css
@import url(http://fonts.googleapis.com/css?family=PT+Serif|PT+Serif:b|PT+Serif:i|PT+Sans|PT+Sans:b);
html {
min-width: 1040px;
}
.ocks-org body {
background: #fcfcfa;
color: #333;
font-family: "PT Serif", serif;
margin: 1em auto 4em auto;
position: relative;
width: 960px;
}
.ocks-org header,
.ocks-org footer,
.ocks-org aside,
.ocks-org h1,
.ocks-org h2,
.ocks-org h3,
.ocks-org h4 {
font-family: "PT Sans", sans-serif;
}
.ocks-org h1,
.ocks-org h2,
.ocks-org h3,
.ocks-org h4 {
color: #000;
}
.ocks-org header,
.ocks-org footer {
color: #636363;
}
h1 {
font-size: 64px;
font-weight: 300;
letter-spacing: -2px;
margin: .3em 0 .1em 0;
}
h2 {
margin-top: 2em;
}
h1, h2 {
text-rendering: optimizeLegibility;
}
h2 a[name],
h2 a[id] {
color: #ccc;
left: -20px;
position: absolute;
width: 740px;
}
header,
footer {
font-size: small;
}
.ocks-org header aside,
.ocks-org footer aside {
float: left;
margin-right: .5em;
}
.ocks-org header aside:after,
.ocks-org footer aside:after {
padding-left: .5em;
content: "/";
}
footer {
margin-top: 8em;
}
h1 ~ aside {
font-size: small;
right: 0;
position: absolute;
width: 180px;
}
.attribution {
font-size: small;
margin-bottom: 2em;
}
body > p, li > p {
line-height: 1.5em;
}
body > p {
width: 720px;
}
body > blockquote {
width: 640px;
}
blockquote q {
display: block;
font-style: oblique;
}
li {
width: 680px;
}
a {
color: steelblue;
}
a:not(:hover) {
text-decoration: none;
}
pre, code, textarea {
font-family: "Menlo", monospace;
}
code {
line-height: 1em;
}
textarea {
font-size: 100%;
}
body > pre {
border-left: solid 2px #ccc;
padding-left: 18px;
margin: 2em 0 2em -20px;
}
.html .value,
.javascript .string,
.javascript .regexp {
color: #756bb1;
}
.html .tag,
.css .tag,
.javascript .keyword {
color: #3182bd;
}
.comment {
color: #636363;
}
.html .doctype,
.javascript .number {
color: #31a354;
}
.html .attribute,
.css .attribute,
.javascript .class,
.javascript .special {
color: #e6550d;
}
svg {
font: 10px sans-serif;
}
.axis path, .axis line {
fill: none;
stroke: #000;
shape-rendering: crispEdges;
}
sup, sub {
line-height: 0;
}
q:before {
content: "“";
}
q:after {
content: "”";
}
blockquote:before {
position: absolute;
left: 2em;
}
blockquote:after {
position: absolute;
}
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