epsilon_hypergraph {HyperG}

Epsilon-Ball Hypergraph

Description

Build a hypergraph by constructing hyperedges from balls around a set of points.

Usage

epsilon_hypergraph(x, epsilon, method = "Euclidean", reduce=FALSE, 
   as.graph=FALSE)

Arguments

x

a matrix of points.

epsilon

radius of the balls. May be a vector.

method

passed to dist to define the distance function.

reduce

logical. Whether to reduce the hypergraph by removing reduntant hyper-edges.

as.graph

logical. Whether to return a graph instead of a hypergraph.

Details

Each point of x corresponds to a vertex in the hypergraph. For each point, a ball of radius epsilon is constructed, and all points in the ball form a hyper-edge in the graph. If epsilon is a vector, each ball may have a different radius, and if the length of epsilon is less than the number of points, they are repeated.

If reduce=TRUE reduntant hyper-edges (those contained in other hyper-edges) are removed. If as.graph==TRUE, reduce is ignored an a graph is returned instead of a hypergraph.

Value

a hypergraph or graph.

Note

Because of symmetry (a is in the ball centered at b if and only if b is in the ball centered at a), the incidence matrix of an epsilon hypergraph is square and symmetric. It can thus be interpreted as an adjacency matrix, and it is this graph that is returned if as.graph==TRUE.

Author(s)

David J. Marchette [e-mail].

See Also

knn_hypergraph, sample_geom_hypergraph, dist.

Examples

   set.seed(565)
	x <- matrix(rnorm(100),ncol=2)
	h <- epsilon_hypergraph(x,epsilon=.25)
	
	   plot(h)
		plot(h,layout=x)
	
	epsilons <- runif(nrow(x),0,.5)
	k <- epsilon_hypergraph(x,epsilon=epsilons)
	
	   plot(k)
		plot(k,layout=x)