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"BalloonEmbedding" (Graph Layout Method)

  • Vertex layout for GraphLayout.
  • Use balloon embedding to lay out vertices of a graph.

Details & Suboptions

  • The balloon embedding is a graph-drawing technique to position vertices of a graph on a circle with the center at the parent vertex.
  • The balloon embedding is typically used to lay out tree graphs.
  • Possible settings to control the layout include:
  • "EvenAngle"Automaticvertices placed evenly in an enclosing circle
    "OptimalOrder"Trueoptimal ordering of vertices to minimize edge crossings
    "RootVertex"Automaticroot vertex
    "SectorAngles"Automaticsize of the angle of each sector
    "Rotation"Automaticlayout rotation

Examples

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Basic Examples  (2)

Place each vertex in an enclosing circle centered at its parent vertex:

Wolfram Language code: Graph[Table[Floor[j / 12]j, {j, 1, 30}], GraphLayout -> "BalloonEmbedding"]

"BalloonEmbedding" works best for tree graphs:

Wolfram Language code: TreeGraph[RandomInteger[{1, #}]  # + 1 & /@ Range[30], GraphLayout -> "BalloonEmbedding"]

Options  (5)

"EvenAngle"  (1)

Use the option "EvenAngle"True to place vertices evenly in an enclosing circle:

Wolfram Language code: {KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "EvenAngle" -> True}], KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "EvenAngle" -> False}]}

"OptimalOrder"  (1)

With the setting "OptimalOrder"True, the vertex ordering optimizes the angular resolution and the aspect ratio:

Wolfram Language code: {KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "OptimalOrder" -> True}], KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "OptimalOrder" -> False}]}

"RootVertex"  (1)

Use the option "RootVertex"v to set the root vertex:

Wolfram Language code: {KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "RootVertex" -> 1}], KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "RootVertex" -> 2}]}

"Rotation"  (1)

Use "Rotation"r to rotate the layout:

Wolfram Language code: KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "Rotation" -> 30 Degree}]

"SectorAngles"  (1)

Use "SectorAngles"s to control the size of each sector:

Wolfram Language code: KaryTree[48, 5, GraphLayout -> {"BalloonEmbedding", "SectorAngles" -> {1 -> Pi / 2}}]