Chapter 06Hierarchal Models

D3’s hierarchy module provides methods to model hierarchal data in memory as node and link objects and to layout (compute coordinates for) the nodes. In this chapter we discuss model construction and the properties and methods of the node object. In subsequent chapters we discuss the layout methods that are available in the module.

Model Construction

The d3.hierarchy(data[,children]) method builds a model of hierarchal data in memory. The method has two parameters, the first one is an object containing hierarchal data and the second is an optional function that takes an object as an argument and returns an array of child objects.

When the d3.hierarchal method is called, it considers the first argument as the root object and creates a node for it. If a second function argument is passed to the method, it is called with the root object as an argument so that it can determine the children of the root node. If the second argument is omitted, the following default function is used to determine the children of the root.

function children(obj) {
  return obj.children;

After d3.hierarchy obtains the array of children for the root object, it creates nodes for each child object and then recursively calls the function argument (or default function) with each of the child objects as an argument.

Below is hierarchal data that is represented in JSON format. The root object with name “A” has 3 children in an array named “children”.   Within that array are 3 objects with names “B”, “C”, and “D”.  The object with name “C” also has children with the names “E” and “F”.

  var data = {"name":"A", "size":1, "children":[
                 {"name":"B", "size":2},
                 {"name":"C", "size":3, "children":[
                     {"name":"E", "size":5},
                     {"name":"F", "size":6}]},
                 {"name":"D", "size":4}]};

The d3.hierarchy method returns a node object representing the root which we can save in a variable.

var root = d3.hierarchy(data);

We show in the screenshot below the root node as returned by d3.hierarchy.

Node Properties

Each node in the hierarchal model has the following properties.

Associated Links and Related Nodes

The node object has various methods that return either an array of associated links or an array of related nodes.


The node object also has a copy method.

Applying a Function to Each Node in a Subtree

The each, eachBefore, and eachAfter methods invoke an argument function for each descendant node.

In the example below we have a hierarchal object consisting of 6 nodes. Each node has a size property. After we construct a root node by calling hierarchy we call each on the root node which causes all of the nodes below the root node to be traversed. When each node is traversed the number stored in the node’s size property along with a space character is concatenated to a string. After the subtree has been traversed, the string is displayed in a div element.

  var data = {"name":"A", "size":1, "children":[
                 {"name":"B", "size":2},
                 {"name":"C", "size":3, "children":[
                     {"name":"E", "size":5},
                     {"name":"F", "size":6}]},
                 {"name":"D", "size":4}]};

  var root = d3.hierarchy(data);
  var count = root.descendants().length;
  var i = 0;

  var text = "";
  root.each((d) => text += + ((++i < count) ? ", " : " "));"#eachText").html(text);

<div id="eachText"></div>

Setting the Value Property

The sum and count methods are used to set each descendant node’s value property. This property is used by some layout methods like d3.treemap.

The sum method is an accumulator method. It traverses the subtree, rooted at the node on which the method is invoked, in postorder traversal order. This ensures that all child nodes are traversed before a parent node. When a node is traversed, the function argument is called and the object in the current node’s data property is passed to the function. The nodes value property is then set to the arithmetic sum of the number returned by the value_function and the numbers in its children’s value properties.

Stated another way, the sum method evaluates the leaf nodes first, setting their value properties to the values returned by the value function. As the traversal moves up the subtree, each node’s value property is set to the sum of the value returned by the value function and the values of the node’s children’s value properties.

Consider the following example.

root.sum((d) => d.size);"#sumText").html("root.value: " + root.value);

<div id="sumText"></div>

When we call sum, we pass it a function. The function takes as an argument the object in the node’s data property and in our example, returns the number in the object’s size property, which is accumulated with the values of its children.

  (d) => d.size

When called, sum will create a new property named value in each node. For each node, the value property will be set to the sum of the number returned by the value function (when called for the node) and the numbers stored in the value properties of the node’s children.

After sum is called, we see that the root node’s value property has the value 21, the sum of 1,2,3,4,5 and 6.


The sort method is often called prior to calling a layout method so that the children in the hierarchy are ordered before coordinates for the nodes are computed.

The comparator function takes 2 nodes as arguments and returns a negative number if the first node should be before the second node, returns a negative number if the second node should be before the first node, and returns 0 if the order doesn’t matter.

The d3 documentation includes sort functions that can be used for circle-packing, treemaps, icicles, trees, and dendrograms.

As a final example in this chapter we reverse the order of each node’s children.

  text = "";
  i = 0;

  root.sort((a,b) => -
  .each((d) => text += + ((++i < count) ? ", " : ""));"#sortText").html(text);

<div id="sortText"></div>