equivalent.hypergraphs {HyperG}

Equivalent Hypergraphs

Description

Test whether two hypergraphs are equivalent. This is not an isomorphism test, merely a test that the incidence matrices are "the same" in the vertex/edge order in which they are resented.

Usage

equivalent.hypergraphs(h1, h2, vertex.names = FALSE, edge.names = FALSE, 
	strip.names=FALSE,
   method = c("any", "exact", "binary"))
as.binary.hypergraph(h)

Arguments

h, h1, h2

hypergraphs.

vertex.names

logical. Whether to ensure the vertex names are all the same.

edge.names

logical. Whether to ensure the hyper-edge names are all the same.

strip.names

logical. Whether to strip the row/column names from the incidence matrices (after ordering them) prior to the equivalence check.

method

see Details.

Details

If either vertex.names or edge.names is TRUE, they are checked for equality, and the incidence matrices are reordered accordingly. The method "exact" checks for the matrices being exactly equal, while "binary" converts all non-zero entries to 1 before the check. The former is for future versions in the event that weighted or directed hypergraphs are implemented. If strip.names is TRUE, the row/column names are stripped from the matrices. If either vertex.names or edge.names is TRUE, the matrices are first ordered according to the rows/columns as appropriate. Note that "binary" will always be TRUE if "exact" is TRUE, and that if "binary" is FALSE, then so will "exact" be.

The method "any" calls the code with strip.names=TRUE and all combinations of vertex.names and edge.names for the binary method, and returns the logical OR of these. Essentially, this tests that the matrices are "the same" under any reasonable interpretation (without checking for equivalence under any reordering except for lexicographic ordering of the row/column names).

Value

a logical in the case of equivalent.hypergraphs, a hypergraph in the case of as.binary.hypergraph.

Author(s)

David J. Marchette [e-mail]

Examples

    h1 <- hypergraph_from_edgelist(list(1:4,2:7,c(1,3,5,7),c(2,4,6)))
    h2 <- hypergraph_from_edgelist(list(letters[1:4],letters[2:7],
	           letters[c(1,3,5,7)],letters[c(2,4,6)]))
    equivalent.hypergraphs(h1,h2)  ## TRUE
    equivalent.hypergraphs(h1,h2,vertex.names=TRUE)  ## FALSE