This function computes the matrix of pairwise distances between all the elements of the two samples put together. The cardinality of the fist sample is denoted by $$n_1$$ and that of the second one is denoted by $$n_2$$.

## Usage

dist_nvd(
x,
y = NULL,
distance = "frobenius",
matching_iterations = 0,
target_matrix = NULL
)

## Arguments

x

A base::list of igraph::igraph objects or matrix representations of underlying networks from a given first population.

y

A base::list of igraph::igraph objects or matrix representations of underlying networks from a given second population.

representation

A string specifying the desired type of representation, among: "adjacency", "laplacian", "modularity" or "graphon". Default is "laplacian".

distance

A string specifying the chosen distance for calculating the test statistic, among: "hamming", "frobenius", "spectral" and "root-euclidean". Default is "frobenius".

matching_iterations

An integer value specifying the maximum number of runs when looking for the optimal permutation for graph matching. Defaults to 0L in which case no matching is done.

target_matrix

A square numeric matrix of size n equal to the order of the graphs specifying a target matrix towards which the initial doubly stochastic matrix is shrunk each time the graph matching algorithm fails to provide a good minimum. Defaults to NULL in which case the target matrix is automatically chosen between the identity matrix or the uniform matrix on the n-simplex.

## Value

A matrix of dimension $$(n_1+n_2) \times (n_1+n_2)$$ containing the distances between all the elements of the two samples put together.

## Examples

gnp_params <- list(p = 1/3)
k_regular_params <- list(k = 8L)
x <- nvd(model = "gnp", n = 10L, model_params = gnp_params)
y <- nvd(model = "k_regular", n = 10L, model_params = k_regular_params)
#>            1         2         3         4         5         6         7
#> 2  1.6182188
#> 3  2.3346721 1.8292590
#> 4  1.1531221 1.5285844 2.5969306
#> 5  0.8849856 1.2821958 2.2823249 1.0825085
#> 6  1.1944673 1.2631468 2.4347225 1.1013615 1.1837482
#> 7  1.4816634 1.6130956 2.7044969 1.1519232 1.4293345 1.1551931
#> 8  1.2675737 1.6677161 2.7477164 1.1587275 1.0161804 1.4433108 1.7222259
#> 9  1.5200807 2.2334176 3.3293784 1.2728087 1.5360785 1.5198496 1.5080376
#> 10 1.1989887 1.8202534 2.7900044 1.2341221 1.4323267 1.2228828 1.2262272
#> 11 1.3799029 1.2210804 2.2104139 1.4272643 1.2482246 1.3794947 1.5615544
#> 12 1.5065074 1.4035111 2.4710310 1.3771665 1.3514119 1.4426534 1.7548539
#> 13 1.4777033 1.2213123 2.0421018 1.5941241 1.2728615 1.4757652 1.6173610
#> 14 1.6664067 1.5421312 2.5617738 1.6018197 1.6861799 1.3584400 1.2822114
#> 15 1.4427592 1.1229369 2.1406727 1.3791808 1.2686269 1.1478232 1.4754556
#> 16 1.4327936 1.4111002 2.4645590 1.3333968 1.2160554 1.3709074 1.3885566
#> 17 1.4648136 1.2742107 2.2761069 1.4325438 1.2693468 1.3526787 1.5062059
#> 18 1.5270568 1.4930275 2.3607668 1.6232515 1.3603132 1.5680684 2.0364625
#> 19 1.3928919 1.5892228 2.3596383 1.5310815 1.2051446 1.6146943 1.8975035
#> 20 1.7283923 1.4877085 2.3210077 1.4488521 1.3263064 1.5835656 1.6908042
#>            8         9        10        11        12        13        14
#> 2
#> 3
#> 4
#> 5
#> 6
#> 7
#> 8
#> 9  1.5010048
#> 10 1.4222375 1.3748589
#> 11 1.4823946 1.9455131 1.4660343
#> 12 1.4864470 2.0268137 1.5520215 1.0716433
#> 13 1.4769877 2.0357477 1.5942977 0.8594279 1.2982404
#> 14 1.8755046 2.0566363 1.4582723 1.2956923 1.3396139 1.3400074
#> 15 1.5533715 1.9264916 1.5444548 0.8429685 1.0458866 0.7268204 1.2391291
#> 16 1.4852218 1.9958873 1.5289911 0.9200683 1.0118756 1.1940376 1.1871331
#> 17 1.5338335 2.0371814 1.4846165 0.7740232 1.0488428 1.0707331 1.3950533
#> 18 1.5877497 2.1721092 1.7670378 1.1324135 0.9822233 1.3807056 1.6875522
#> 19 1.5269017 2.1036968 1.7910394 1.1033057 1.0519179 1.4021658 1.5831592
#> 20 1.4956007 2.0057310 1.7761849 1.1231756 1.1355052 1.3252517 1.6285054
#>           15        16        17        18        19
#> 2
#> 3
#> 4
#> 5
#> 6
#> 7
#> 8
#> 9
#> 10
#> 11
#> 12
#> 13
#> 14
#> 15
#> 16 1.0022083
#> 17 0.8794542 0.6886927
#> 18 1.1450239 1.3628452 1.1477949
#> 19 1.2047551 0.8621763 1.0255236 1.2025500
#> 20 1.0938690 1.0275766 0.9739499 1.2014374 1.1457005