NestGraph

NestGraph[f,expr,n]

gives the graph obtained by starting with expr and applying f successively n times.

NestGraph[f,{expr1,expr2,…},n]

gives the graph obtained by applying f to expr1, expr2, ….

NestGraph[f,graph,n]

gives the graph obtained by applying f to the vertices of graph and extending the graph.

Details and Options

  • NestGraph is also known as crawl graph or tree growing.
  • expr can be an expression or a list of expressions or graphs.
  • NestGraph[f,expr] is equivalent to NestGraph[f,expr,1].
  • NestGraph[f,expr] gives a graph with edges {exprexpr1,…,exprexprk}, where f[expr] evaluates to {expr1,…,exprk}.
  • NestGraph[f,{expr1,expr2,…}] is the graph union of NestGraph[f,expr1] and NestGraph[f,expr2],….
  • NestGraph[f,graph] is the union of graph and NestGraph[f,{v1,…}], where vi are the vertices of graph.
  • NestGraph[f,graph,n] is the union of NestGraph[f,graph,n-1] and NestGraph[f,{v1,…}], where vi are the vertices of NestGraph[f,graph,n-1].
  • NestGraph[f,expr,n] is equivalent to NestGraph[f,graph,n], where graph is the singleton graph with only one vertex expr and no edges.
  • NestGraph takes the same options as Graph.
  • The option DirectedEdges can be used to control whether an undirected or directed graph is constructed.

Examples

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Basic Examples  (4)

Construct a graph by starting with x and applying f successively 3 times:

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The function to nest can be a pure function:

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Generate a binary tree of nested functions:

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Generate a graph of neighboring countries around Switzerland:

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Scope  (3)

Options  (80)

Applications  (2)

Properties & Relations  (5)

Neat Examples  (1)

Introduced in 2015
(10.2)