LambdaComponents
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
open all close allScope (6)
LambdaComponents works with undirected graphs:
Give the components that include at least one of the vertices:
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:
Text
Wolfram Research (2012), LambdaComponents, Wolfram Language function, https://reference.wolfram.com/language/ref/LambdaComponents.html (updated 2015).
CMS
Wolfram Language. 2012. "LambdaComponents." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/LambdaComponents.html.
APA
Wolfram Language. (2012). LambdaComponents. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LambdaComponents.html