LambdaComponents

LambdaComponents[g]

gives the lambda components of the graph g.

LambdaComponents[g,{v1,v2,}]

gives the lambda components that include at least one of the vertices {v1,v2,}.

LambdaComponents[{vw,},]

uses rules vw to specify the graph g.

Details

  • LambdaComponents is also known as a lambda set.
  • A lambda component is a set of vertices that have more edge-independent paths connecting them to each other than to outside vertices.
  • LambdaComponents returns a list of components {c1,c2,}, where each component ci is given as a list of vertices.
  • LambdaComponents[g] is equivalent to LambdaComponents[g,VertexList[g]].
  • LambdaComponents works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (1)

Give the lambda components for a graph:

Scope  (6)

LambdaComponents works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Give the components that include at least one of the vertices:

Use rules to specify the graph:

Applications  (2)

Highlight all lambda components in a graph:

A family network consisting of the closest relatives, including parents, siblings, and children. Find a smallest family group with more than one member, where relatives have more edge-independent paths connecting them to each other than to relatives outside the group:

The first nontrivial λ component occurs after the singletons:

Properties & Relations  (2)

All LuccioSami components are lambda components:

The converse is not always true:

Lambda components are partially ordered by inclusion:

The corresponding directed acyclic graph:

Introduced in 2012
 (9.0)
 |
Updated in 2014
 (10.0)
2015
 (10.3)