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"HyperbolicSpringEmbedding" (Graph Layout Method)

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

Details & Options

  • The hyperbolic spring embedding is a graph-drawing technique to position vertices of a graph on the Poincaré disk so that they minimize the mechanical energy when each edge corresponds to a spring.
  • The hyperbolic spring embedding is typically used to lay out tree-like structured graphs.
  • The following graph parameters can be given:
  • "EdgeWeighted" whether to use edge weights
  • Possible settings to control the energy minimization process include:
  • "EnergyControl"how the energy function is controlled during minimization
    "MaxIteration"maximum number of iterations
    "RandomSeed"seed for the random generator for initial vertex placement
    "StepControl"how step lengths are modified during energy minimization
    "StepLength"initial step length used in moving the vertices
    "Tolerance"tolerance used in terminating the process

Examples

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Basic Examples  (1)

Place vertices on a Poincaré disk:

Wolfram Language code: KaryTree[30, GraphLayout -> "HyperbolicSpringEmbedding"]

Options  (8)

"EdgeWeighted"  (1)

With the setting "EdgeWeighted"True, edge weights are used:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 10]; weight = RandomInteger[{1, 5}, 11];
Wolfram Language code: Graph[edge, EdgeWeight -> weight, GraphLayout -> {"HyperbolicSpringEmbedding", "EdgeWeighted" -> #}]& /@ {True, False}

"EnergyControl"  (1)

Use the option "EnergyControl"e to specify limitations on the total energy of the system during minimization:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 30];
Wolfram Language code: Graph[edge, {GraphLayout -> {"HyperbolicSpringEmbedding", "EnergyControl" -> #}}]& /@ {Automatic, "Monotonic", "NonMonotonic"}

"InferentialDistance"  (1)

Use "InferentialDistance"d to specify a cutoff distance beyond which the interaction between vertices is assumed to be nonexistent:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 30];
Wolfram Language code: Graph[edge, GraphLayout -> {"HyperbolicSpringEmbedding", "InferentialDistance" -> #}]& /@ {Automatic, .5, 2}

"MaxIteration"  (1)

Use "MaxIteration"it to specify a maximum number of iterations to be used in attempting to minimize the energy:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 30];
Wolfram Language code: Graph[edge, GraphLayout -> {"HyperbolicSpringEmbedding", "MaxIteration" -> #}]& /@ {Automatic, 1, 2}

"RandomSeed"  (1)

Use "RandomSeed"int to specify a seed for the random number generator that computes the initial vertex placement:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 30];
Wolfram Language code: Graph[edge, GraphLayout -> {"HyperbolicSpringEmbedding", "RandomSeed" -> #}]& /@ {1, 5}

"StepControl"  (1)

Use "StepControl"method to define how step length is modified during energy minimization:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 30];
Wolfram Language code: Graph[edge, GraphLayout -> {"HyperbolicSpringEmbedding", "StepControl" -> #}]& /@ {Automatic, "Monotonic", "NonMonotonic", "StrictlyMonotonic"}

"StepLength"  (1)

Use "StepLength"r to specify the initial step length used in moving the vertices around:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 30];
Wolfram Language code: Graph[edge, GraphLayout -> {"HyperbolicSpringEmbedding", "StepLength" -> #}]& /@ {1, 4.5}

"Tolerance"  (1)

Use "Tolerance"r to specify the tolerance used in terminating the energy minimization process:

Wolfram Language code: edge = RandomInteger[#]# + 1& /@ Range[0, 30];
Wolfram Language code: Graph[edge, GraphLayout -> {"HyperbolicSpringEmbedding", "Tolerance" -> #}]& /@ {Automatic, .5}