sample_geom_hypergraph: Construct a hypergraph from a random collection of points.
In HyperG: Hypergraphs in R

Description Usage Arguments Details Value Note Author(s) See Also Examples

A hypergraph defined by the relationships amongst a set of points.

sample_geom_hypergraph(n, m, d = 2, X, Y, radius,method = "Euclidean",
thresh.method="leq", uniformly = FALSE)
plot_geom_hypergraph(h, pch = 20, cex = 3, col = "gray",
plotY = TRUE, plot.circles = plotY,
full.circles=TRUE,
lty = 2, lcol = "black", ...)

`n`	The number of points to generate (ignored if `X` is provided). This corresponds to the number of vertices in the hypergraph.
`m`	The number of nodes in the hypergraph (ignored if `Y` is provided). This corresponds to the number of hyper-edges in the hypergraph.
`d`	dimension of the points (ignored if both `X` and `Y` are provided).
`radius,uniformly`	see Description.
`X`	see Description.
`Y`	see Description.
`method`	method passed to `dist`.
`thresh.method`	if this is 'leq' then hyper-edges are defined by whether the Y points are a distance less than or equal to the radius. If 'geq', then it is determined by greater than. Any other value will default to 'leq'.
`h`	a hypergraph generated by `sample_geom_hypergraph`.
`plotY`	logical. Whether to plot the `Y` variables defining the hypergaph.
`pch,cex,col`	parameters controling the plotting of `Y`.
`plot.circles,full.circles`	logical. Whether to plot the circles defining the hyper-edges. If `full.circles` is TRUE, the plot limits are set so that the complete circles are plotted. Otherwise they may be clipped.
`lty,lcol`	parameters controling the plotting of the circles.
`...`	parameters passed to `plot`.

If either X or Y is missing, it is generated as a set of d-dimensional points in the unit cube, n points in X, m points in Y. If X is given, then n is ignored. Similary with Y and m. If both are given, then d is ignored. There is no checking that the provided X and/or Y matrices conform to the n,m,d values given in the call.

The inter-point distance matrix is computed using dist as proxy::dist(Y,X,method=method). If radius is not provided, it is chosen uniformly at random from the unique values of the distance matrix if uniformly is FALSE, and uniformly from between the minimum and maximum distance if uniformly is true. As a rule, one should not let this function choose the radius, but the code will do so if you wish. The matrix is then thresholded by the radius, resulting in a binary matrix which is then used as the mxn incidence matrix for the hypergraph.

a hypergraph. Additionally, the defining vectors X and Y and the radius are returned as named values of the hypergraph.

If both X and Y are given, and R is not given, a random value for R is chosen randomly from the unique inter-point distances. If all three of these variables are provided, the hypergraph is not random.

David J. Marchette dmarchette@gmail.com

dist.

	set.seed(235)
   h <- sample_geom_hypergraph(100,20,radius=0.2)
	set.seed(3519)
	Y <- matrix(runif(20),ncol=2)
	X <- do.call(rbind,
	     lapply(1:nrow(Y),function(i) cbind(rnorm(10,Y[i,1]),rnorm(10,Y[i,2]))))
	

   h <- sample_geom_hypergraph(X=X,Y=Y,radius=0.2)