This is a collection of functions that provide statistics for testing equality in distribution between samples of networks.

## Usage

```
stat_student_euclidean(d, indices, ...)
stat_welch_euclidean(d, indices, ...)
stat_original_edge_count(d, indices, edge_count_prep, ...)
stat_generalized_edge_count(d, indices, edge_count_prep, ...)
stat_weighted_edge_count(d, indices, edge_count_prep, ...)
```

## Arguments

- d
Either a matrix of dimension \((n1+n2)x(n1+n2)\) containing the distances between all the elements of the two samples put together (for distance-based statistics) or the concatenation of the lists of matrix representations of networks in samples 1 and 2 for Euclidean t-Statistics.

- indices
A vector of dimension \(n1\) containing the indices of the elements of the first sample.

- ...
Extra parameters specific to some statistics.

- edge_count_prep
A list of preprocessed data information used by edge count statistics and produced by

`edge_count_global_variables`

.

## Details

In details, there are three main categories of statistics:

*Euclidean t-Statistics*: both Student`stat_student_euclidean`

version for equal variances and Welch`stat_welch_euclidean`

version for unequal variances,*Statistics based on similarity graphs*: 3 types of edge count statistics.

## Examples

```
n1 <- 30L
n2 <- 10L
gnp_params <- list(p = 1/3)
k_regular_params <- list(k = 8L)
x <- nvd(model = "gnp", n = n1, model_params = gnp_params)
y <- nvd(model = "k_regular", n = n2, model_params = k_regular_params)
r <- repr_nvd(x, y, representation = "laplacian")
stat_student_euclidean(r, 1:n1)
#> [1] 0.8055932
stat_welch_euclidean(r, 1:n1)
#> [1] 0.9542853
d <- dist_nvd(x, y, representation = "laplacian", distance = "frobenius")
ecp <- edge_count_global_variables(d, n1, k = 5L)
stat_original_edge_count(d, 1:n1, edge_count_prep = ecp)
#> [1] -5.644431
stat_generalized_edge_count(d, 1:n1, edge_count_prep = ecp)
#> [1] 37.37713
stat_weighted_edge_count(d, 1:n1, edge_count_prep = ecp)
#> [1] -0.3640767
```