sample_geom_hypergraph {HyperG}

Construct a hypergraph from a random collection of points.

Description

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

Usage

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", ...)

Arguments

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.

Details

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.

Value

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

Note

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.

Author(s)

David J. Marchette [e-mail]

See Also

dist.

Examples

	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)