# Hierarchical Drawing of Directed Graphs

LayeredGraphPlot attempts to draw the vertices of a graph in a series of layers, placing dominant vertices at the top, and vertices lower in the hierarchy progressively further down.

LayeredGraphPlot[{v_{i1}->v_{j1},v_{i2}->v_{j2},...}] |

| generate a layered plot of the graph in which vertex is connected to vertex |

LayeredGraphPlot[{{v_{i1}->v_{j1},lbl_{1}},...}] |

| associate labels with edges in the graph |

LayeredGraphPlot[g,pos] | place the dominant vertices in the plot at position pos |

LayeredGraphPlot[m] | generate a layered plot of the graph represented by the adjacency matrix m |

Hierarchical graph drawing.

LayeredGraphPlot draws a graph so that the edges point predominantly downward. The second argument of

LayeredGraphPlot specifies the position of the root. Possible values for this argument are

Right,

Left,

Top, and

Bottom.

This plots a directed graph.

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This is the same graph, with edges pointing from left to right.

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LayeredGraphPlot may produce slightly different output on different platforms, due to floating-point differences.

## Options for LayeredGraphPlot

In addition to options for

Graphics, the following options are accepted for

LayeredGraphPlot.

Options for LayeredGraphPlot.

### DirectedEdges

The option

DirectedEdges specifies whether to draw edges as arrows. Possible values for this option are

True or

False. The default value for this option is

True.

This shows a graph with edges represented by lines instead of arrows.

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### EdgeLabeling

The option

EdgeLabeling specifies whether and how to display labels given for the edges. Possible values for this option are

True,

False, or

Automatic. The default value for this option is

True, which displays the supplied edge labels on the graph. With

EdgeLabeling->Automatic, the labels are shown as tooltips.

This displays the specified edge label.

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This displays the labels as tooltips. Place the cursor over the edge between vertices 3 and 6 to see the tooltip.

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Alternatively, use

Tooltip to specify a tooltip for an edge. Place the cursor over the edge between vertices 3 and 6, as well as the edge label on the edge between vertices 3 and 5, to see the tooltips.

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### EdgeRenderingFunction

The option

EdgeRenderingFunction specifies graphical representation of the graph edges. Possible values for this option are

Automatic,

None, or a function that gives a proper combination of graphics primitives and directives. With the default setting of

Automatic, a dark red line is drawn for each edge. With

EdgeRenderingFunction->None, edges are not drawn.

This draws vertices only.

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With

EdgeRenderingFunction->g, each edge is rendered with the graphics primitives and directives given by the function

g. It can take three or more arguments in the form

, where

,

are the coordinates of the beginning and ending points of the edge,

,

are the beginning and ending vertices, and

is any label specified for the edge or

None. Explicit settings for

EdgeRenderingFunction->g override settings for

EdgeLabeling and

DirectedEdges.

This plots edges as gray arrows with ends set back from vertices by a distance of 0.3 (in the graph's coordinate system).

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### MultiedgeStyle

The option

MultiedgeStyle specifies whether to draw multiple edges between two vertices. Possible values for

MultiedgeStyle are

Automatic (the default),

True,

False, or a positive real number. With the default setting

MultiedgeStyle->Automatic, multiple edges are shown for a graph specified by a list of rules, but not shown if the graph is specified by an adjacency matrix. With

MultiedgeStyle->, the multiedges are spread out to a scaled distance of

.

By default, multiple edges are shown if a graph is given as a list of rules.

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But multiple edges are not shown for graphs specified by an adjacency matrix.

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This spreads multiple edges by the specified amount.

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#### PackingMethod

The option

PackingMethod specifies the method used for packing disconnected components. Possible values for the option are

Automatic (the default),

,

,

,

,

, and

. With

PackingMethod, components are packed as close together as possible using a polyomino method [

6], starting from the top left. With

PackingMethod, components are packed starting from the center. With

PackingMethod, components are packed in layers starting from top left. With

PackingMethod or

PackingMethod, components are packed in layers starting from the top/left, respectively. With

PackingMethod, components are arranged in a nested grid. The typical effective default setting is

PackingMethod, and the packing starts with components of the largest bounding box area.

This shows the packing of disconnected components by the default method.

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This shows the packing of disconnected components using the

method.

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### PlotRangePadding

PlotRangePadding is a common option for graphics functions inherited by

LayeredGraphPlot.

### PlotStyle

PlotStyle is a common option for graphics functions inherited by

LayeredGraphPlot. The option

PlotStyle specifies the style in which objects are drawn.

Draw edges with thicker arrows, and both edges and vertices' labels in red.

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### SelfLoopStyle

The option

SelfLoopStyle specifies whether and how to draw loops for vertices that are linked to themselves. Possible values of the option are

Automatic (the default),

True,

False, or a positive real number. With

SelfLoopStyle->Automatic, self-loops are shown if the graph is specified by a list of rules, but not by an adjacency matrix. With

SelfLoopStyle->, the self-loops are drawn with a diameter of

(relative to the average edge length).

By default, self-loops are displayed for a graph specified by a list of rules.

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Self-loops are not shown if the graph is specified by an adjacency matrix.

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This shows self-loops with diameter equal to 0.3 times the average length of the edges.

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### VertexCoordinateRules

The option

VertexCoordinateRules specifies the coordinates of the vertices. Possible values are

None, or a list of coordinates. Coordinates specified by a list of rules are not currently supported by

LayeredGraphPlot.

This draws the Petersen graph using known coordinates.

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This draws with the default method.

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### VertexLabeling

The option

VertexLabeling specifies whether to show vertex names as labels. Possible values for this option are

True,

False,

Automatic (the default) and

Tooltip.

VertexLabeling shows the labels. For graphs specified by an adjacency matrix, vertex labels are taken to be successive integers

, where

n is the size of the matrix. For graphs specified by a list of rules, labels are the expressions used in the rules.

VertexLabeling->False displays each vertex as a point.

VertexLabeling->Tooltip displays each vertex as a point, but gives its name in a tooltip.

VertexLabeling->Automatic displays each vertex as a point, giving its name in a tooltip if the number of vertices is not too large. You can also use

Tooltip anywhere in the list of rules to specify an alternative tooltip for a vertex

.

This draws the graph with labels given as indices of the adjacency matrix.

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This uses the labels specified in the list of rules.

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This plots vertices as points, and displays vertex names in tooltips. Place the cursor above the vertices to see the labels.

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### VertexRenderingFunction

The option

VertexRenderingFunction specifies graphical representation of the graph edges. Possible values for this option are

Automatic,

None, or a function that gives a proper combination of graphics primitives and directives. With the default setting of

Automatic, vertices are displayed as points, with their names given in tooltips.

By default, vertices are displayed as points and, for small graphs, labeled in tooltips. Point the cursor at a vertex to see the tooltip.

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This draws the same graph, but without the vertices.

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With

VertexRenderingFunction->g, each vertex is rendered with the graphics primitives given by

, where

is the coordinate of the vertex and

is the label of the vertex. Explicit settings for

VertexRenderingFunction->g override settings for

VertexLabeling.

This shows vertices as yellow disks.

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## Example Gallery

### Flow Chart

LayeredGraphPlot helps visualize flow charts, for example for business, economic, or technical presentations.

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This shows a flow chart that flows from left to right.

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### Food Chains

Food chains can be visualized with

LayeredGraphPlot.

This shows a small food chain.

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This shows another food chain.

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### History of Unix

LayeredGraphPlot is suitable for visualizing historical events.

This shows a history of Unix.

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