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TikZ and PGF Manual

TikZ

21 Making Trees Grow

21.1 Introduction to the Child Operation

Trees are a common way of visualizing hierarchical structures. A simple tree looks like this:

(-tikz- diagram)

Admittedly, in reality trees are more likely to grow upward and not downward as above. You can tell whether the author of a paper is a mathematician or a computer scientist by looking at the direction their trees grow. A computer scientist’s trees will grow downward while a mathematician’s tree will grow upward. Naturally, the correct way is the mathematician’s way, which can be specified as follows:

(-tikz- diagram)


\begin{tikzpicture}
\node {root} [grow'=up]
child {node {left}}
child {node {right}
child {node {child}}
child {node {child}}
};
\end{tikzpicture}

In TikZ, there are two ways of specifying trees: Using either the graph path operation, which is covered in Section 19, or using the child path operation, which is covered in the present section. Both methods have their advantages.

In TikZ, trees are specified by adding children to a node on a path using the child operation:

21.2 Child Paths and Child Nodes

For each child of a root node, its child path is inserted at a specific location in the picture (the placement rules are discussed in Section 21.5). The first node in the child path, if it exists, is special and called the child node. If there is no first node in the child path, that is, if the child path is missing (including the curly braces) or if it does not start with node or with coordinate, then an empty child node of shape coordinate is automatically added.

Consider the example \node {x} child {node {y}} child;. For the first child, the child path has the child node node {y}. For the second child, no child node is specified and, thus, it is just coordinate.

As for any normal node, you can give the child node a name, shift it around, or use options to influence how it is rendered.

(-tikz- diagram)

\usetikzlibrary {shapes.geometric}
\begin{tikzpicture}[sibling distance=15mm]
\node[rectangle,draw] {root}
child {node[circle,draw,yshift=-5mm] (left node) {left}}
child {node[ellipse,draw] (right node) {right}};
\draw[dashed,->] (left node) -- (right node);
\end{tikzpicture}

In many cases, the child path will just consist of a specification of a child node and, possibly, children of this child node. However, the node specification may be followed by arbitrary other material that will be added to the picture, transformed to the child’s coordinate system. For your convenience, a move-to (0,0) operation is inserted automatically at the beginning of the path. Here is an example:

(-tikz- diagram)


\begin{tikzpicture}
\node {root}
child {[fill] circle [radius=2pt]}
child {[fill] circle [radius=2pt]};
\end{tikzpicture}

At the end of the child path you may add a special path operation called edge from parent. If this operation is not given by yourself somewhere on the path, it will be automatically added at the end. This option causes a connecting edge from the parent node to the child node to be added to the path. By giving options to this operation you can influence how the edge is rendered. Also, nodes following the edge from parent operation will be placed on this edge, see Section 21.6 for details.

To sum up:

  • 1. The child path starts with a node specification. If it is not there, it is added automatically.

  • 2. The child path ends with a edge from parent operation, possibly followed by nodes to be put on this edge. If the operation is not given at the end, it is added automatically.

21.3 Naming Child Nodes

Child nodes can be named like any other node using either the name option or the special syntax in which the name of the node is placed in round parentheses between the node operation and the node’s text.

If you do not assign a name to a child node, TikZ will automatically assign a name as follows: Assume that the name of the parent node is, say, parent. (If you did not assign a name to the parent, TikZ will do so itself, but that name will not be user-accessible.) The first child of parent will be named parent-1, the second child is named parent-2, and so on.

This naming convention works recursively. If the second child parent-2 has children, then the first of these children will be called parent-2-1 and the second parent-2-2 and so on.

If you assign a name to a child node yourself, no name is generated automatically (the node does not have two names). However, “counting continues”, which means that the third child of parent is called parent-3 independently of whether you have assigned names to the first and/or second child of parent.

Here is an example:

(-tikz- diagram)


\begin{tikzpicture}[sibling distance=15mm]
\node (root) {root}
child
child {
child {coordinate (special)}
child
};
\node at (root-1) {root-1};
\node at (root-2) {root-2};
\node at (special) {special};
\node at (root-2-2) {root-2-2};
\end{tikzpicture}
21.4 Specifying Options for Trees and Children

Each child may have its own options, which apply to “the whole child”, including all of its grandchildren. Here is an example:

(-tikz- diagram)


\begin{tikzpicture}
[thick,level 1/.style={sibling distance=15mm},
level 2/.style={sibling distance=10mm}]
\coordinate
child[red] {child child}
child[green] {child child[blue]};
\end{tikzpicture}

The options of the root node have no effect on the children since the options of a node are always “local” to that node. Because of this, the edges in the following tree are black, not red.

(-tikz- diagram)


\begin{tikzpicture}[thick]
\node [red] {root}
child
child;
\end{tikzpicture}

This raises the problem of how to set options for all children. Naturally, you could always set options for the whole path as in \path [red] node {root} child child; but this is bothersome in some situations. Instead, it is easier to give the options before the first child as follows:

(-tikz- diagram)


\begin{tikzpicture}[thick]
\node [red] {root}
[green] % option applies to all children
child
child;
\end{tikzpicture}

Here is the set of rules:

  • 1. Options for the whole tree are given before the root node.

  • 2. Options for the root node are given directly to the node operation of the root.

  • 3. Options for all children can be given between the root node and the first child.

  • 4. Options applying to a specific child path are given as options to the child operation.

  • 5. Options applying to the node of a child, but not to the whole child path, are given as options to the node command inside the child path.


\begin{tikzpicture}
\scoped
[...] % Options apply to the whole tree
\node[...] {root} % Options apply to the root node only
[...] % Options apply to all children
child[...] % Options apply to this child and all its children
{
node[...] {} % Options apply to the child node only
...
}
child[...] % Options apply to this child and all its children
;
\end{tikzpicture}

There are additional styles that influence how children are rendered:

  • /tikz/every child(style, initially empty)

  • This style is used at the beginning of each child, as if you had given the style’s contents as options to the child operation.

21.5 Placing Child Nodes
21.5.1 Basic Idea

Perhaps the most difficult part in drawing a tree is the correct layout of the children. Typically, the children have different sizes and it is not easy to arrange them in such a manner that not too much space is wasted, the children do not overlap, and they are either evenly spaced or their centers are evenly distributed. Calculating good positions is especially difficult since a good position for the first child may depend on the size of the last child.

In basic TikZ, when you do not make use of the graph drawing facilities explained in Part IV, a comparatively simple approach is taken to placing the children. In order to compute a child’s position, all that is taken into account is the number of the current child in the list of children and the number of children in this list. Thus, if a node has five children, then there is a fixed position for the first child, a position for the second child, and so on. These positions do not depend on the size of the children and, hence, children can easily overlap. However, since you can use options to shift individual children a bit, this is not as great a problem as it may seem.

Although the placement of the children only depends on their number in the list of children and the total number of children, everything else about the placement is highly configurable. You can change the distance between children (appropriately called the sibling distance) and the distance between levels of the tree. These distances may change from level to level. The direction in which the tree grows can be changed globally and for parts of the tree. You can even specify your own “growth function” to arrange children on a circle or along special lines or curves.

21.5.2 Default Growth Function

The default growth function works as follows: Assume that we are given a node and five children. These children will be placed on a line with their centers (or, more generally, with their anchors) spaced apart by the current sibling distance. The line is orthogonal to the current direction of growth, which is set with the grow and grow' option (the latter option reverses the ordering of the children). The distance from the line to the parent node is given by the level distance.

(-tikz- diagram)


\begin{tikzpicture}[sibling distance=15mm, level distance=15mm]
\path [help lines]
node (root) {root}
[grow=-10]
child {node {1}}
child {node {2}}
child {node {3}}
child {node {4}};

\draw[|<->|,thick] (root-1.center)
-- node[above,sloped] {sibling distance} (root-2.center);

\draw[|<->|,thick] (root.center)
-- node[above,sloped] {level distance} +(-10:\tikzleveldistance);
\end{tikzpicture}
21.5.3 Missing Children

Sometimes one or more of the children of a node are “missing”. Such a missing child will count as a child with respect to the total number of children and also with respect to the current child count, but it will not be rendered.

21.5.4 Custom Growth Functions
21.6 Edges From the Parent Node

Every child node is connected to its parent node via a special kind of edge called the edge from parent. This edge is added to the child path when the following path operation is encountered: