Document singular value scaling for undirected graphs

[alexpghayes]

Scratch code

library(fastRG)
library(tidyverse)

n <- 200

k <- 5
B <- matrix(0.01, nrow = k, ncol = k)
diag(B) <- 0.8

pi <- rep(1 / k, k)


m <- fastRG::dcsbm(
  theta = stats::runif(n, min = 1, max = 3),
  B = B,
  pi = pi
)



EA <- m$X %*% m$S %*% t(m$X)
pop_s <- svds(EA, k)
pop_s$d

sum(EA)

A <- sample_sparse(m)
expected_edges(m)
sum(triu(A))

s <- svds(m)
s$d

expected_edges(m)
sum(triu(sample_sparse(m)))

once <- function() {
  sqrt(svds(sample_sparse(m), k)$d)
}

num_reps <- 50
samp <- do.call(rbind, map(1:num_reps, ~once()))

colnames(samp) <- paste0("d", 1:k)

true <- tibble(
  value = sqrt(s$d * 2),
  space = paste0("d", 1:k)
)

as_tibble(samp) |> 
  pivot_longer(
    cols = contains("d"),
    names_to = "space"
  ) |> 
  ggplot(aes(value)) +
  geom_histogram() +
  geom_vline(data = true, mapping = aes(xintercept = value)) +
  scale_fill_viridis_d() +
  facet_grid(
    rows = vars(space),
    scales = "free_x"
  ) +
  theme_minimal()