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```
```use itertools::Itertools;
use num_integer::binomial;
use petgraph::{Graph, Undirected};
use rand::distributions::Distribution;
use rand::seq::IteratorRandom;
use rand::Rng;
use std::iter::FromIterator;
use thiserror::Error;

#[derive(Debug, Error, PartialEq)]
pub enum UniformGraphError {
#[error("too many edges")]
TooManyEdges,
}

#[derive(Debug, Clone)]
pub struct UniformGraphDistribution {
nodes: usize,
edges: usize,
}

impl UniformGraphDistribution {
/// Creates a new `UniformGraphDistribution` with `nodes` nodes, and `edges` edges.
///
/// Will return an error if `edges > binomial(nodes, 2)`.
///
/// # Example
/// ```rust
/// use random_graphs::prelude::*;
/// use rand::prelude::*;
///
/// let distribution = UniformGraphDistribution::new(4, 2).unwrap();
///
/// // Generate a random graph
/// let graph = distribution.sample(&mut thread_rng());
/// assert_eq!(graph.node_count(), 4);
/// assert_eq!(graph.edge_count(), 2);
/// ```
pub fn new(nodes: usize, edges: usize) -> Result<Self, UniformGraphError> {
// Cannot have more than C(N, 2) edges in a graph on N edges.
if edges > binomial(nodes, 2) {
return Err(UniformGraphError::TooManyEdges);
}

Ok(Self { nodes, edges })
}
}

impl Distribution<Graph<usize, (), Undirected>> for UniformGraphDistribution {
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Graph<usize, (), Undirected> {
let mut graph = Graph::with_capacity(self.nodes, self.edges);

// Add all of our nodes to the graph
let nodes = Vec::from_iter((0..self.nodes).map(|i| graph.add_node(i)));

let chosen_edges = nodes
.iter()
.cartesian_product(nodes.iter())
// Don't want to have self-loops, so filter out any (node, node) pairs
.filter(|(node, other_node)| node != other_node)
.choose_multiple(rng, self.edges);

for (edge_start, edge_end) in chosen_edges {
graph.add_edge(*edge_start, *edge_end, ());
}

graph
}
}

#[cfg(test)]
mod test {
use super::*;
use petgraph::prelude::EdgeRef;
use rand::thread_rng;

#[test]
fn test_invalid_edge_count_causes_error() {
// In an undirected graph on 4 nodes, there are at most 6 edges (count them, I dare you!)
let distribution = UniformGraphDistribution::new(4, 6);
assert!(distribution.is_ok());

let distribution = UniformGraphDistribution::new(4, 7);
assert_eq!(distribution.err(), Some(UniformGraphError::TooManyEdges));
}

#[test]
fn test_uniform_graph_distribution() {
let nodes = 4;
let edges = 2;

let distribution = UniformGraphDistribution::new(nodes, edges).unwrap();
let mut rng = thread_rng();

let mut edge_buckets = vec![vec![0; nodes]; nodes];

for _ in 0..10000 {
let graph = distribution.sample(&mut rng);
assert_eq!(graph.node_count(), nodes);
assert_eq!(graph.edge_count(), edges);

for edge in graph.edge_references() {
let src_index = edge.source().index();
let tgt_index = edge.target().index();

// Graph has no self loops
assert_ne!(src_index, tgt_index);

edge_buckets[src_index][tgt_index] += 1;
}
}

let minimum_bucket_size = edge_buckets
.iter()
.enumerate()
.map(|(index, inner_bucket)| {
inner_bucket
.iter()
.enumerate()
.filter(|(inner_index, _)| *inner_index != index)
.min()
.unwrap()
.clone()
})
.map(|(_, inner_min)| *inner_min)
.min()
.unwrap();

let maximum_bucket_size = edge_buckets
.iter()
.enumerate()
.map(|(index, inner_bucket)| {
inner_bucket
.iter()
.enumerate()
.filter(|(inner_index, _)| *inner_index != index)
.max()
.unwrap()
.clone()
})
.map(|(_, inner_max)| *inner_max)
.max()
.unwrap();

// TODO: use the power of mathematics to determine the probability of obtaiing
//  results at least as extreme as the one we did, assuming a uniform distribution
//  with 10,000 samples.
let relative_delta =
((maximum_bucket_size - minimum_bucket_size) as f32) / (minimum_bucket_size as f32);
assert!(relative_delta < 0.10);
}
}
```