DPmatching {GMPro}

calculate degree profile distances between two graphs and match nodes.

Description

This function constructs empirical distributions of degree profiles for each vertex and then calculate distances between each pair of vertices, one from graph A and the other from graph B. The default used is the 1-Wasserstein distance. This function also matches vertices in A with vertices in B via the distance matrix between A and B. The distance matrix can be null and DPmatching will calculate it. A and B cannot be null when the distance matrix is null.

Usage

DPmatching(A, B, W = NULL)

Arguments

A, B

Two 0/1 adjacency matrices.

W

A distance matrix between A and B, which can be null. If null, this function will calculate it. More details in DPdistance.

Value

Dist

The distance matrix between two graphs.

match

A vector containing matching results.

Examples

set.seed(2020)
n = 10; q = 1/2; s = 1; p = 1
Parent = matrix(rbinom(n*n, 1, q), nrow = n, ncol = n)
Parent[lower.tri(Parent)] = t(Parent)[lower.tri(Parent)]
diag(Parent) <- 0
### Generate graph A
dA = matrix(rbinom(n*n, 1, s), nrow = n, ncol=n);
dA[lower.tri(dA)] = t(dA)[lower.tri(dA)]
A1 = Parent*dA
tmp = rbinom(n, 1, p)
n.A = length(which(tmp == 1))
indA = sample(1:n, n.A, replace = FALSE)
A = A1[indA, indA]
### Generate graph B
dB = matrix(rbinom(n*n, 1, s), nrow = n, ncol=n);
dB[lower.tri(dB)] = t(dB)[lower.tri(dB)]
B1 = Parent*dB
tmp = rbinom(n, 1, p)
n.B = length(which(tmp == 1))
indB = sample(1:n, n.B, replace = FALSE)
B = B1[indB, indB]
DPmatching(A, B)
W = DPdistance(A, B)
DPmatching(A, B, W)