is.star {HyperG}

Is a hypergraph a star?

Description

Tests whether a hypergraph is a star. Finds the minimal intersection set of the hyper-edges.

Usage

is.star(h,type=c("weak","strong"))
intersection_set(h)

Arguments

h

a hypergraph.

type

see Details.

Details

A (weak) star hypergraph is one in which the intersection of all the hyper-edges is non-empty.

An intersection set is a set of vertices that is contained in every edge. The argument type="strong" for is.star indicates that the only vertices which are common between any pair of vertices are contained in the intersection set (or "hub") of the star hypergraph. So a hypergraph that is strongly star is weakly star, but not vice versa.

Value

a logical, for is.star. A set of vertices (or NULL) that are contained in every hyper-edge. This would be the "hub" of the star.

Author(s)

David J. Marchette [e-mail].

References

Akram, M., & Luqman, A. (2020). Fuzzy hypergraphs and related extensions. Springer Singapore.

Examples

h <- hypergraph_from_edgelist(list(c(1:4,16),
		  c(4:7,16),
		  c(4,8:10,16),
		  c(4,10:16),
		  c(4,16)))
is.star(h)  ## TRUE
is.star(h,type='strong')  ## FALSE
intersection_set(h)     ## 4, 16