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use log::info;
use rayon::prelude::*;
use crate::graph::csr::{prefix_sum, Csr, SwapCsr};
use crate::graph::Target;
use crate::index::Idx;
use crate::{
CsrLayout, DirectedDegrees, DirectedNeighborsWithValues, Error, Graph, SharedMut,
UndirectedDegrees, UndirectedNeighborsWithValues,
};
use std::ops::Range;
use std::sync::Arc;
use std::time::Instant;
/// Partition the node set based on the degrees of the nodes.
pub trait DegreePartitionOp<NI: Idx, EV> {
/// Creates a range-based degree partition of the nodes.
///
/// Divide the nodes into `concurrency` number of ranges such that these
/// ranges have roughly equal total degree. That is, the sum of the degrees
/// of the nodes of each range should be roughly equal to the extent that
/// that's actually possible.
/// The length of the returned vector will never exceed `concurrency`.
fn degree_partition(&self, concurrency: usize) -> Vec<Range<NI>>;
}
/// Partition the node set based on the out degrees of the nodes.
pub trait OutDegreePartitionOp<NI: Idx, EV> {
/// Creates a range-based out degree partition of the nodes.
///
/// Divide the nodes into `concurrency` number of ranges such that these
/// ranges have roughly equal total out degree. That is, the sum of the out
/// degrees of the nodes of each range should be roughly equal to the extent
/// that that's actually possible.
/// The length of the returned vector will never exceed `concurrency`.
fn out_degree_partition(&self, concurrency: usize) -> Vec<Range<NI>>;
}
/// Partition the node set based on the in degrees of the nodes.
pub trait InDegreePartitionOp<NI: Idx, EV> {
/// Creates a range-based in degree partition of the nodes.
///
/// Divide the nodes into `concurrency` number of ranges such that these
/// ranges have roughly equal total in degree. That is, the sum of the in
/// degrees of the nodes of each range should be roughly equal to the extent
/// that that's actually possible.
/// The length of the returned vector will never exceed `concurrency`.
fn in_degree_partition(&self, concurrency: usize) -> Vec<Range<NI>>;
}
/// Call a particular function for each node with its corresponding state in parallel.
pub trait ForEachNodeParallelOp<NI: Idx> {
/// For each node calls `node_fn` with the node and its corresponding mutable
/// state in parallel.
///
/// For every node `n` in the graph `node_fn(&self, n, node_values[n.index()])`
/// will be called.
///
/// `node_values` must have length exactly equal to the number of nodes in
/// the graph.
///
/// # Example
///
/// ```
/// # use graph_builder::prelude::*;
/// # use std::ops::Range;
/// let graph: DirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(0, 1), (0, 2), (1, 2)])
/// .build();
/// let mut node_values = vec![0; 3];
///
/// graph.
/// for_each_node_par(&mut node_values, |g, node, node_state| {
/// *node_state = g.out_degree(node);
/// });
///
/// assert_eq!(node_values[0], 2);
/// assert_eq!(node_values[1], 1);
/// assert_eq!(node_values[2], 0);
/// ```
fn for_each_node_par<T, F>(&self, node_values: &mut [T], node_fn: F) -> Result<(), Error>
where
T: Send,
F: Fn(&Self, NI, &mut T) + Send + Sync;
}
/// Call a particular function for each node with its corresponding state in parallel based on a
/// partition.
pub trait ForEachNodeParallelByPartitionOp<NI: Idx> {
/// For each node calls `node_fn` with the node and its corresponding
/// mutable state in parallel, using `partition` as a parallelization hint.
///
/// For every node `n` in the graph `node_fn(&self, n, node_values[n.index()])`
/// will be called.
///
/// `node_values` must have length exactly equal to the number of nodes in
/// the graph.
///
/// The parallelization will be implemented such that the work for a set of
/// nodes represented by each range in `partition` will correspond to a task
/// that will run in a single thread.
///
/// # Example
///
/// ```
/// # use graph_builder::prelude::*;
/// # use std::ops::Range;
/// let graph: DirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(0, 1), (0, 2), (1, 2)])
/// .build();
/// let mut node_values = vec![0; 3];
/// let partition: Vec<Range<u32>> = graph.out_degree_partition(num_cpus::get());
///
/// graph.
/// for_each_node_par_by_partition(&partition, &mut node_values, |g, node, node_state| {
/// *node_state = g.out_degree(node);
/// });
///
/// assert_eq!(node_values[0], 2);
/// assert_eq!(node_values[1], 1);
/// assert_eq!(node_values[2], 0);
/// ```
fn for_each_node_par_by_partition<T, F>(
&self,
partition: &[Range<NI>],
node_values: &mut [T],
node_fn: F,
) -> Result<(), Error>
where
T: Send,
F: Fn(&Self, NI, &mut T) + Send + Sync;
}
pub trait RelabelByDegreeOp<NI, EV> {
/// Creates a new graph by relabeling the node ids of the given graph.
///
/// Ids are relabaled using descending degree-order, i.e., given `n` nodes,
/// the node with the largest degree will become node id `0`, the node with
/// the smallest degree will become node id `n - 1`.
///
/// Note, that this method creates a new graph with the same space
/// requirements as the input graph.
///
/// # Example
///
/// ```
/// use graph_builder::prelude::*;
///
/// let mut graph: UndirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(0, 1), (1, 2), (1, 3), (3, 0)])
/// .build();
///
/// assert_eq!(graph.degree(0), 2);
/// assert_eq!(graph.degree(1), 3);
/// assert_eq!(graph.degree(2), 1);
/// assert_eq!(graph.degree(3), 2);
///
/// let mut neighbors = graph.neighbors(0);
/// assert_eq!(neighbors.next(), Some(&1));
/// assert_eq!(neighbors.next(), Some(&3));
/// assert_eq!(neighbors.next(), None);
///
/// graph.make_degree_ordered();
///
/// assert_eq!(graph.degree(0), 3);
/// assert_eq!(graph.degree(1), 2);
/// assert_eq!(graph.degree(2), 2);
/// assert_eq!(graph.degree(3), 1);
///
/// assert_eq!(graph.neighbors(0).as_slice(), &[1, 2, 3]);
/// ```
fn make_degree_ordered(&mut self);
}
pub trait ToUndirectedOp {
type Undirected;
/// Creates a new undirected graph from the edges of an existing graph.
///
/// Note, that this method creates a new graph with the same space
/// requirements as the input graph.
///
/// # Example
///
/// ```
/// use graph_builder::prelude::*;
///
/// let graph: DirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(0, 1), (2, 0)])
/// .build();
///
/// assert_eq!(graph.out_degree(0), 1);
/// assert_eq!(graph.out_neighbors(0).as_slice(), &[1]);
///
/// assert_eq!(graph.in_degree(0), 1);
/// assert_eq!(graph.in_neighbors(0).as_slice(), &[2]);
///
/// let graph = graph.to_undirected(None);
///
/// assert_eq!(graph.degree(0), 2);
/// assert_eq!(graph.neighbors(0).as_slice(), &[1, 2]);
/// ```
///
/// This method accepts an optional [`CsrLayout`] as second parameter,
/// which has the same effect as described in [`GraphBuilder::csr_layout`]
/// # Example
///
/// ```
/// use graph_builder::prelude::*;
///
/// let graph: DirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(0, 2), (1, 0), (2, 0)])
/// .build();
///
/// // No layout specified, a default layput is chosen
/// let un_graph = graph.to_undirected(None);
/// assert_eq!(un_graph.neighbors(0).as_slice(), &[2, 1, 2]);
///
/// // The `Sorted` layout
/// let un_graph = graph.to_undirected(CsrLayout::Sorted);
/// assert_eq!(un_graph.neighbors(0).as_slice(), &[1, 2, 2]);
///
/// // The `Deduplicated` layout
/// let un_graph = graph.to_undirected(CsrLayout::Deduplicated);
/// assert_eq!(un_graph.neighbors(0).as_slice(), &[1, 2]);
/// ```
fn to_undirected(&self, layout: impl Into<Option<CsrLayout>>) -> Self::Undirected;
}
pub trait SerializeGraphOp<W> {
fn serialize(&self, write: W) -> Result<(), Error>;
}
pub trait DeserializeGraphOp<R, G> {
fn deserialize(read: R) -> Result<G, Error>;
}
impl<G, NI, EV> RelabelByDegreeOp<NI, EV> for G
where
NI: Idx,
EV: Copy + Ord + Sync,
G: Graph<NI>
+ UndirectedDegrees<NI>
+ UndirectedNeighborsWithValues<NI, EV>
+ SwapCsr<NI, NI, EV>
+ Sync,
{
fn make_degree_ordered(&mut self) {
relabel_by_degree(self)
}
}
impl<NI, G> ForEachNodeParallelOp<NI> for G
where
NI: Idx,
G: Graph<NI> + Sync,
{
/// For each node calls a given function with the node and its corresponding
/// mutable state in parallel.
///
/// The parallelization is done by means of a [rayon](https://docs.rs/rayon/)
/// based fork join with a task for each node.
fn for_each_node_par<T, F>(&self, node_values: &mut [T], node_fn: F) -> Result<(), Error>
where
T: Send,
F: Fn(&Self, NI, &mut T) + Send + Sync,
{
if node_values.len() != self.node_count().index() {
return Err(Error::InvalidNodeValues);
}
let node_fn = Arc::new(node_fn);
node_values
.into_par_iter()
.enumerate()
.for_each(|(i, node_state)| node_fn(self, NI::new(i), node_state));
Ok(())
}
}
impl<NI, G> ForEachNodeParallelByPartitionOp<NI> for G
where
NI: Idx,
G: Graph<NI> + Sync,
{
/// For each node calls a given function with the node and its corresponding
/// mutable state in parallel based on the provided node partition.
///
/// The parallelization is done by means of a [rayon](https://docs.rs/rayon/)
/// based fork join with a task for each range in the provided node partition.
fn for_each_node_par_by_partition<T, F>(
&self,
partition: &[Range<NI>],
node_values: &mut [T],
node_fn: F,
) -> Result<(), Error>
where
T: Send,
F: Fn(&Self, NI, &mut T) + Send + Sync,
{
if node_values.len() != self.node_count().index() {
return Err(Error::InvalidNodeValues);
}
if partition.iter().map(|r| r.end - r.start).sum::<NI>() != self.node_count() {
return Err(Error::InvalidPartitioning);
}
let node_fn = Arc::new(node_fn);
let node_value_splits = split_by_partition(partition, node_values);
node_value_splits
.into_par_iter()
.zip(partition.into_par_iter())
.for_each_with(node_fn, |node_fn, (mutable_chunk, range)| {
for (node_state, node) in mutable_chunk.iter_mut().zip(range.start.range(range.end))
{
node_fn(self, node, node_state);
}
});
Ok(())
}
}
impl<NI, EV, U> DegreePartitionOp<NI, EV> for U
where
NI: Idx,
U: Graph<NI> + UndirectedDegrees<NI> + UndirectedNeighborsWithValues<NI, EV>,
{
/// Creates a greedy range-based degree partition of the nodes.
///
/// It is greedy in the sense that it goes through the node set only once
/// and simply adds a new range to the result whenever the current range's
/// nodes' degrees sum up to at least the average node degree.
///
/// # Example
///
/// ```
/// # use graph_builder::prelude::*;
/// # use std::ops::Range;
/// let graph: UndirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(0, 1), (0, 2), (0, 3), (0, 3)])
/// .build();
///
/// let partition: Vec<Range<u32>> = graph.degree_partition(2);
///
/// assert_eq!(partition.len(), 2);
/// assert_eq!(partition[0], 0..1);
/// assert_eq!(partition[1], 1..4);
/// ```
fn degree_partition(&self, concurrency: usize) -> Vec<Range<NI>> {
let batch_size = ((self.edge_count().index() * 2) as f64 / concurrency as f64).ceil();
greedy_node_map_partition(
|node| self.degree(node).index(),
self.node_count(),
batch_size as usize,
concurrency,
)
}
}
impl<NI, EV, D> OutDegreePartitionOp<NI, EV> for D
where
NI: Idx,
D: Graph<NI> + DirectedDegrees<NI> + DirectedNeighborsWithValues<NI, EV>,
{
/// Creates a greedy range-based out degree partition of the nodes.
///
/// It is greedy in the sense that it goes through the node set only once
/// and simply adds a new range to the result whenever the current range's
/// nodes' out degrees sum up to at least the average node out degree.
///
/// # Example
///
/// ```
/// # use graph_builder::prelude::*;
/// # use std::ops::Range;
/// let graph: DirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(0, 1), (0, 2), (2, 1), (2, 3)])
/// .build();
///
/// let partition: Vec<Range<u32>> = graph.out_degree_partition(2);
///
/// assert_eq!(partition.len(), 2);
/// assert_eq!(partition[0], 0..1);
/// assert_eq!(partition[1], 1..4);
/// ```
fn out_degree_partition(&self, concurrency: usize) -> Vec<Range<NI>> {
let batch_size = (self.edge_count().index() as f64 / concurrency as f64).ceil();
greedy_node_map_partition(
|node| self.out_degree(node).index(),
self.node_count(),
batch_size as usize,
concurrency,
)
}
}
impl<NI, EV, D> InDegreePartitionOp<NI, EV> for D
where
NI: Idx,
D: Graph<NI> + DirectedDegrees<NI> + DirectedNeighborsWithValues<NI, EV>,
{
/// Creates a greedy range-based in degree partition of the nodes.
///
/// It is greedy in the sense that it goes through the node set only once
/// and simply adds a new range to the result whenever the current range's
/// nodes' in degrees sum up to at least the average node in degree.
///
/// # Example
///
/// ```
/// # use graph_builder::prelude::*;
/// # use std::ops::Range;
/// let graph: DirectedCsrGraph<u32> = GraphBuilder::new()
/// .edges(vec![(1, 0), (1, 2), (2, 0), (3, 2)])
/// .build();
///
/// let partition: Vec<Range<u32>> = graph.in_degree_partition(2);
///
/// assert_eq!(partition.len(), 2);
/// assert_eq!(partition[0], 0..1);
/// assert_eq!(partition[1], 1..4);
/// ```
fn in_degree_partition(&self, concurrency: usize) -> Vec<Range<NI>> {
let batch_size = (self.edge_count().index() as f64 / concurrency as f64).ceil();
greedy_node_map_partition(
|node| self.in_degree(node).index(),
self.node_count(),
batch_size as usize,
concurrency,
)
}
}
// Split input slice into a vector of partition.len() disjoint slices such that
// the slice at index i in the output vector has the same length as the range at
// index i in the input partition.
fn split_by_partition<'a, NI: Idx, T>(
partition: &[Range<NI>],
slice: &'a mut [T],
) -> Vec<&'a mut [T]> {
debug_assert_eq!(
partition
.iter()
.map(|r| r.end - r.start)
.sum::<NI>()
.index(),
slice.len()
);
let mut splits = Vec::with_capacity(partition.len());
let mut remainder = slice;
let mut current_start = NI::zero();
for range in partition.iter() {
let next_end = range.end - current_start;
current_start += next_end;
let (left, right) = remainder.split_at_mut(next_end.index());
splits.push(left);
remainder = right;
}
splits
}
// Partition nodes 0..node_count().index() into at most max_batches ranges such
// that the sums of node_map(node) for each range are roughly equal. It does so
// greedily and therefore does not guarantee an optimally balanced range-based
// partition.
fn greedy_node_map_partition<NI, F>(
node_map: F,
node_count: NI,
batch_size: usize,
max_batches: usize,
) -> Vec<Range<NI>>
where
F: Fn(NI) -> usize,
NI: Idx,
{
let mut partitions = Vec::with_capacity(max_batches);
let mut partition_size = 0;
let mut partition_start = NI::zero();
let upper_bound = node_count - NI::new(1);
for node in NI::zero().range(node_count) {
partition_size += node_map(node);
if (partitions.len() < max_batches - 1 && partition_size >= batch_size)
|| node == upper_bound
{
let partition_end = node + NI::new(1);
partitions.push(partition_start..partition_end);
partition_size = 0;
partition_start = partition_end;
}
}
partitions
}
fn relabel_by_degree<NI, G, EV>(graph: &mut G)
where
NI: Idx,
G: Graph<NI>
+ UndirectedDegrees<NI>
+ UndirectedNeighborsWithValues<NI, EV>
+ SwapCsr<NI, NI, EV>
+ Sync,
EV: Copy + Ord + Sync,
{
let start = Instant::now();
let degree_node_pairs = sort_by_degree_desc(graph);
info!("Relabel: sorted degree-node-pairs in {:?}", start.elapsed());
let start = Instant::now();
let (degrees, nodes) = unzip_degrees_and_nodes(degree_node_pairs);
info!("Relabel: built degrees and id map in {:?}", start.elapsed());
let start = Instant::now();
let offsets = prefix_sum(degrees);
let targets = relabel_targets(graph, nodes, &offsets);
info!("Relabel: built and sorted targets in {:?}", start.elapsed());
graph.swap_csr(Csr::new(
offsets.into_boxed_slice(),
targets.into_boxed_slice(),
));
}
// Extracts (degree, node_id) pairs from the given graph and sorts them by
// degree descending.
fn sort_by_degree_desc<NI, EV, G>(graph: &G) -> Vec<(NI, NI)>
where
NI: Idx,
G: Graph<NI> + UndirectedDegrees<NI> + UndirectedNeighborsWithValues<NI, EV> + Sync,
{
let node_count = graph.node_count().index();
let mut degree_node_pairs = Vec::with_capacity(node_count);
(0..node_count)
.into_par_iter()
.map(NI::new)
.map(|node_id| (graph.degree(node_id), node_id))
.collect_into_vec(&mut degree_node_pairs);
degree_node_pairs.par_sort_unstable_by(|left, right| left.cmp(right).reverse());
degree_node_pairs
}
// Unzips (degree, node-id) pairs into `degrees` and `nodes`
//
// `degrees` maps a new node id to its degree.
// `nodes` maps the previous node id to the new node id.
fn unzip_degrees_and_nodes<NI: Idx>(degree_node_pairs: Vec<(NI, NI)>) -> (Vec<NI>, Vec<NI>) {
let node_count = degree_node_pairs.len();
let mut degrees = Vec::<NI>::with_capacity(node_count);
let mut nodes = Vec::<NI>::with_capacity(node_count);
let nodes_ptr = SharedMut::new(nodes.as_mut_ptr());
(0..node_count)
.into_par_iter()
.map(|n| {
let (degree, node) = degree_node_pairs[n];
// SAFETY: node is the node_id from degree_node_pairs which is
// created from 0..node_count -- the values are all distinct and we
// will not write into the same location in parallel
unsafe {
nodes_ptr.add(node.index()).write(NI::new(n));
}
degree
})
.collect_into_vec(&mut degrees);
// SAFETY: degree_node_pairs contains each value in 0..node_count once
unsafe {
nodes.set_len(node_count);
}
(degrees, nodes)
}
// Relabel target ids according to the given node mapping and offsets.
fn relabel_targets<NI, EV, G>(graph: &G, nodes: Vec<NI>, offsets: &[NI]) -> Vec<Target<NI, EV>>
where
NI: Idx,
G: Graph<NI> + UndirectedNeighborsWithValues<NI, EV> + Sync,
EV: Copy + Ord + Sync,
{
let node_count = graph.node_count().index();
let edge_count = offsets[node_count].index();
let mut targets = Vec::<Target<NI, EV>>::with_capacity(edge_count);
let targets_ptr = SharedMut::new(targets.as_mut_ptr());
(0..node_count).into_par_iter().map(NI::new).for_each(|u| {
let new_u = nodes[u.index()];
let start_offset = offsets[new_u.index()].index();
let mut end_offset = start_offset;
for &v in graph.neighbors_with_values(u) {
let new_v = nodes[v.target.index()];
// SAFETY: a node u is processed by at most one thread. We write
// into a non-overlapping range defined by the offsets for that
// node. No two threads will write into the same range.
unsafe {
targets_ptr
.add(end_offset)
.write(Target::new(new_v, v.value));
}
end_offset += 1;
}
// SAFETY: start_offset..end_offset is a non-overlapping range for
// a node u which is processed by exactly one thread.
unsafe {
std::slice::from_raw_parts_mut(targets_ptr.add(start_offset), end_offset - start_offset)
}
.sort_unstable();
});
// SAFETY: we inserted every relabeled target id of which there are edge_count many.
unsafe {
targets.set_len(edge_count);
}
targets
}
#[cfg(test)]
mod tests {
use crate::{
builder::GraphBuilder, graph::csr::UndirectedCsrGraph, graph_ops::unzip_degrees_and_nodes,
UndirectedNeighbors,
};
use super::*;
#[test]
fn split_by_partition_3_parts() {
let partition = vec![0..2, 2..5, 5..10];
let mut slice = (0..10).collect::<Vec<_>>();
let splits = split_by_partition(&partition, &mut slice);
assert_eq!(splits.len(), partition.len());
for (s, p) in splits.into_iter().zip(partition) {
assert_eq!(s, p.into_iter().collect::<Vec<usize>>());
}
}
#[test]
fn split_by_partition_8_parts() {
let partition = vec![0..1, 1..2, 2..3, 3..4, 4..6, 6..7, 7..8, 8..10];
let mut slice = (0..10).collect::<Vec<_>>();
let splits = split_by_partition(&partition, &mut slice);
assert_eq!(splits.len(), partition.len());
for (s, p) in splits.into_iter().zip(partition) {
assert_eq!(s, p.into_iter().collect::<Vec<usize>>());
}
}
#[test]
fn greedy_node_map_partition_1_part() {
let partitions = greedy_node_map_partition::<usize, _>(|_| 1_usize, 10, 10, 99999);
assert_eq!(partitions.len(), 1);
assert_eq!(partitions[0], 0..10);
}
#[test]
fn greedy_node_map_partition_2_parts() {
let partitions = greedy_node_map_partition::<usize, _>(|x| x % 2_usize, 10, 4, 99999);
assert_eq!(partitions.len(), 2);
assert_eq!(partitions[0], 0..8);
assert_eq!(partitions[1], 8..10);
}
#[test]
fn greedy_node_map_partition_6_parts() {
let partitions = greedy_node_map_partition::<usize, _>(|x| x, 10, 6, 99999);
assert_eq!(partitions.len(), 6);
assert_eq!(partitions[0], 0..4);
assert_eq!(partitions[1], 4..6);
assert_eq!(partitions[2], 6..7);
assert_eq!(partitions[3], 7..8);
assert_eq!(partitions[4], 8..9);
assert_eq!(partitions[5], 9..10);
}
#[test]
fn greedy_node_map_partition_max_batches() {
let partitions = greedy_node_map_partition::<usize, _>(|x| x, 10, 6, 3);
assert_eq!(partitions.len(), 3);
assert_eq!(partitions[0], 0..4);
assert_eq!(partitions[1], 4..6);
assert_eq!(partitions[2], 6..10);
}
#[test]
fn sort_by_degree_test() {
let graph: UndirectedCsrGraph<_> = GraphBuilder::new()
.edges::<u32, _>(vec![
(0, 1),
(1, 2),
(1, 3),
(2, 0),
(2, 1),
(2, 3),
(3, 0),
(3, 2),
])
.build();
assert_eq!(
sort_by_degree_desc(&graph),
vec![(5, 2), (4, 3), (4, 1), (3, 0)]
);
}
#[test]
fn unzip_degrees_and_nodes_test() {
let degrees_and_nodes = vec![(5, 2), (4, 3), (4, 1), (3, 0)];
let (degrees, nodes) = unzip_degrees_and_nodes::<u32>(degrees_and_nodes);
assert_eq!(degrees, vec![5, 4, 4, 3]);
assert_eq!(nodes, vec![3, 2, 0, 1]);
}
#[test]
fn relabel_by_degree_test() {
let mut graph: UndirectedCsrGraph<_> = GraphBuilder::new()
.edges::<u32, _>(vec![
(0, 1),
(1, 2),
(1, 3),
(2, 0),
(2, 1),
(2, 3),
(3, 0),
(3, 2),
])
.build();
graph.make_degree_ordered();
assert_eq!(graph.node_count(), graph.node_count());
assert_eq!(graph.edge_count(), graph.edge_count());
// old -> new
// 0 -> 3
// 1 -> 2
// 2 -> 0
// 3 -> 1
assert_eq!(graph.degree(0), 5);
assert_eq!(graph.degree(1), 4);
assert_eq!(graph.degree(2), 4);
assert_eq!(graph.degree(3), 3);
assert_eq!(graph.neighbors(0).as_slice(), &[1, 1, 2, 2, 3]);
assert_eq!(graph.neighbors(1).as_slice(), &[0, 0, 2, 3]);
assert_eq!(graph.neighbors(2).as_slice(), &[0, 0, 1, 3]);
assert_eq!(graph.neighbors(3).as_slice(), &[0, 1, 2]);
}
}