Added methods to 'Connected' calculating eccentricity, radius, diamter, and centers.

Author: Emoun

src/algo/dijkstra_shortest_paths.rs

@@ -9,25 +9,25 @@ where
 {
 	graph: &'a G,
 	visited: Vec<G::Vertex>,
-	// We keep is sorted with the lowest weight at the end for efficiency.
+	// We keep it sorted with the lowest weight at the end for efficiency.
 	queue: Vec<(W, (G::Vertex, G::Vertex, &'a G::EdgeWeight))>,
-	get_weight: fn(&G::EdgeWeight) -> W,
+	get_distance: fn(&G::EdgeWeight) -> W,
 }
 
 impl<'a, G, W> DijkstraShortestPaths<'a, G, W>
 where
 	G: 'a + Graph,
 	W: PrimInt + Unsigned,
 {
-	pub fn new(graph: &'a G, get_weight: fn(&G::EdgeWeight) -> W) -> Self
+	pub fn new(graph: &'a G, get_distance: fn(&G::EdgeWeight) -> W) -> Self
 	where
 		G: HasVertex,
 	{
 		let mut dijk = Self {
 			graph,
 			visited: Vec::new(),
 			queue: Vec::new(),
-			get_weight,
+			get_distance,
 		};
 		dijk.visit(graph.get_vertex(), W::zero());
 		dijk
@@ -43,7 +43,7 @@ where
 
 		for (sink, weight) in edges
 		{
-			let new_weight = w + (self.get_weight)(weight);
+			let new_weight = w + (self.get_distance)(weight);
 			if let Some((old_weight, old_edge)) = self
 				.queue
 				.iter_mut()
@@ -62,6 +62,26 @@ where
 		}
 		self.queue.sort_by(|(w1, _), (w2, _)| w2.cmp(w1));
 	}
+
+	/// Returns the vertices reachable from the designated vertex and the
+	/// weighted distance to them
+	pub fn distances(
+		graph: &'a G,
+		get_distance: fn(&G::EdgeWeight) -> W,
+	) -> impl 'a + Iterator<Item = (G::Vertex, W)>
+	where
+		G: HasVertex,
+		W: 'a,
+	{
+		let mut distances = vec![(graph.get_vertex(), W::zero())];
+
+		DijkstraShortestPaths::new(graph, get_distance).map(move |(so, si, w)| {
+			let dist = distances.iter().find(|(v, _)| so == *v).unwrap().1;
+			let new_dist = dist + get_distance(w);
+			distances.push((si, new_dist));
+			(si, new_dist)
+		})
+	}
 }
 
 impl<'a, G> DijkstraShortestPaths<'a, G, G::EdgeWeight>

src/core/edge.rs

@@ -5,7 +5,7 @@
 /// For undirected graphs, which vertex is which has no meaning.
 /// For directed graphs, an edge points from the `source` to the `sink`.
 ///
-/// This trait has a blanket implementation implementation for any pair `(V,V)`
+/// This trait has a blanket implementation for any pair `(V,V)`
 /// or triple `(V,V,W)`. Therefore, the easiest way to create an edge is to
 /// simply use a pair. The triple can be used if the edge is weighted
 pub trait Edge<V>

src/core/graph.rs

@@ -51,7 +51,7 @@ pub trait Graph
 {
 	/// Type of the graphs vertices.
 	///
-	/// This type should be lightweight, as its passed around by-value
+	/// This type should be lightweight, as it's passed around by-value
 	/// (therefore must implement [`Copy`](https://doc.rust-lang.org/std/marker/trait.Copy.html)).
 	/// Whether two vertices are equal is also a very common operation and
 	/// should therefore also be light-weight.

src/core/property/connected.rs

@@ -1,21 +1,116 @@
 use crate::{
-	algo::Dfs,
+	algo::{Dfs, DijkstraShortestPaths},
 	core::{
 		property::{
-			proxy_remove_edge_where_weight, proxy_remove_vertex, DirectedGraph, HasVertexGraph,
-			RemoveEdge, RemoveVertex, Unilateral, Weak,
+			proxy_remove_edge_where_weight, proxy_remove_vertex, DirectedGraph, EdgeCount,
+			HasVertex, HasVertexGraph, RemoveEdge, RemoveVertex, Unilateral, VertexInGraph, Weak,
 		},
 		proxy::ReverseGraph,
 		Ensure, Graph, GraphDerefMut,
 	},
 };
+use num_traits::{PrimInt, Unsigned};
 use std::borrow::Borrow;
 
 /// A marker trait for graphs that are connected.
 ///
 /// A graph is connected if there is a path from any vertex to any other vertex.
 /// Graphs with one or zero vertices count as connected.
-pub trait Connected: Unilateral {}
+pub trait Connected: Unilateral
+{
+	/// Calculates the maximum distance between the designated vertex and any other vertex ([the eccentricity](https://mathworld.wolfram.com/GraphEccentricity.html)).
+	///
+	/// Takes a closure that converts an edge's weight into a distance value.
+	/// The distance between two vertices is equal to the distance of the
+	/// edge(s) between them.
+	fn eccentricity_weighted<W: PrimInt + Unsigned>(
+		&self,
+		get_distance: fn(&Self::EdgeWeight) -> W,
+	) -> W
+	where
+		Self: EdgeCount + HasVertex + Sized,
+	{
+		// We search for all the shortest paths, the eccentricity is the longest one
+		DijkstraShortestPaths::distances(self, get_distance).fold(W::zero(), |max_dist, (_, d2)| {
+			if max_dist < d2
+			{
+				d2
+			}
+			else
+			{
+				max_dist
+			}
+		})
+	}
+
+	/// Calculates the maximum eccentricity of the graph ([the diameter](https://mathworld.wolfram.com/GraphDiameter.html)).
+	///
+	/// Takes a closure that converts an edge's weight into a distance value.
+	/// The distance between two vertices is equal to the distance of the
+	/// edge(s) between them.
+	fn diameter_weighted<W: PrimInt + Unsigned>(
+		&self,
+		get_distance: fn(&Self::EdgeWeight) -> W,
+	) -> W
+	where
+		Self: EdgeCount + Sized,
+	{
+		self.all_vertices().fold(W::zero(), |max_ecc, v| {
+			let new_ecc =
+				VertexInGraph::ensure_unvalidated(self, v).eccentricity_weighted(get_distance);
+			if new_ecc > max_ecc
+			{
+				new_ecc
+			}
+			else
+			{
+				max_ecc
+			}
+		})
+	}
+
+	/// Calculates the minimum eccentricity of the graph ([the radius](https://mathworld.wolfram.com/GraphDiameter.html)).
+	///
+	/// Takes a closure that converts an edge's weight into a distance value.
+	/// The distance between two vertices is equal to the distance of the
+	/// edge(s) between them.
+	fn radius_weighted<W: PrimInt + Unsigned>(&self, get_distance: fn(&Self::EdgeWeight) -> W) -> W
+	where
+		Self: EdgeCount + Sized,
+	{
+		self.all_vertices().fold(W::zero(), |min_ecc, v| {
+			let new_ecc =
+				VertexInGraph::ensure_unvalidated(self, v).eccentricity_weighted(get_distance);
+			if new_ecc < min_ecc
+			{
+				new_ecc
+			}
+			else
+			{
+				min_ecc
+			}
+		})
+	}
+
+	/// Returns the vertices with eccentricity equal to the radius ([the centers](https://mathworld.wolfram.com/GraphCenter.html)).
+	///
+	/// Takes a closure that converts an edge's weight into a distance value.
+	/// The distance between two vertices is equal to the distance of the
+	/// edge(s) between them.
+	fn centers_weighted<'a, W: 'a + PrimInt + Unsigned>(
+		&'a self,
+		get_distance: fn(&Self::EdgeWeight) -> W,
+	) -> impl Iterator<Item = Self::Vertex> + '_
+	where
+		Self: EdgeCount + Sized,
+	{
+		let radius = self.radius_weighted(get_distance);
+		self.all_vertices().filter(move |v| {
+			VertexInGraph::ensure_unvalidated(self, *v).eccentricity_weighted(get_distance)
+				== radius
+		})
+	}
+}
 
 #[derive(Clone, Debug)]
 pub struct ConnectedGraph<C: Ensure>(C);

src/core/property/has_vertex.rs

@@ -22,7 +22,7 @@ pub trait HasVertex: Graph
 /// Ensures the underlying graph has at least 1 vertex.
 ///
 /// Gives no guarantees on which vertex is returned by any given call to
-/// `get_vertex` if the the graph has multiple vertices.
+/// `get_vertex` if the graph has multiple vertices.
 #[derive(Clone)]
 pub struct HasVertexGraph<C: Ensure>(C);
 

src/core/property/impl_ensurer.rs

@@ -395,6 +395,44 @@ macro_rules! impl_properties {
 			}
 		}
 
+		// VertexCount
+		$crate::impl_properties!{
+			@struct [ $struct ]
+			@generic [ $($generics)* ]
+			@delegate [ $delegate_type ]
+			$(@exclude [ $($exclude_props)* ])?
+			$(@include [ $($include_props)* ])?
+			@bounds [
+				<$delegate_type as $crate::core::GraphDeref>::Graph:
+					$crate::core::property::VertexCount,
+				$($bounds)*
+			]
+			@trait_id VertexCount [$crate::core::property]
+			@implement {
+				type Count = <<$delegate_type as $crate::core::GraphDeref>::Graph
+					as $crate::core::property::VertexCount>::Count;
+			}
+		}
+
+		// EdgeCount
+		$crate::impl_properties!{
+			@struct [ $struct ]
+			@generic [ $($generics)* ]
+			@delegate [ $delegate_type ]
+			$(@exclude [ $($exclude_props)* ])?
+			$(@include [ $($include_props)* ])?
+			@bounds [
+				<$delegate_type as $crate::core::GraphDeref>::Graph:
+					$crate::core::property::EdgeCount,
+				$($bounds)*
+			]
+			@trait_id EdgeCount [$crate::core::property]
+			@implement {
+				type Count = <<$delegate_type as $crate::core::GraphDeref>::Graph
+					as $crate::core::property::EdgeCount>::Count;
+			}
+		}
+
 		// Unique
 		$crate::impl_properties!{
 			@struct [ $struct ]

tests/core/property/connectedness.rs

@@ -5,12 +5,15 @@ use crate::mock_graph::{
 	MockDirectedness, MockEdgeWeight, MockGraph, MockVertexWeight,
 };
 use duplicate::duplicate_item;
-use graphene::core::{
-	property::{
-		AddEdge, Connected, ConnectedGraph, HasVertex, NewVertex, RemoveEdge, RemoveVertex,
-		Unilateral, UnilateralGraph, VertexInGraph, Weak, WeakGraph,
+use graphene::{
+	algo::DijkstraShortestPaths,
+	core::{
+		property::{
+			AddEdge, Connected, ConnectedGraph, HasVertex, NewVertex, RemoveEdge, RemoveVertex,
+			Unilateral, UnilateralGraph, VertexInGraph, Weak, WeakGraph,
+		},
+		Directed, Graph, Undirected,
 	},
-	Directed, EnsureUnloaded, ReleaseUnloaded, Undirected,
 };
 use static_assertions::assert_impl_all;
 
@@ -47,6 +50,7 @@ use static_assertions::assert_impl_all;
 mod module
 {
 	use super::*;
+	use graphene::core::{EnsureUnloaded, ReleaseUnloaded};
 
 	/// Tests that the graph correctly identifies graphs with its connectedness.
 	#[quickcheck]
@@ -227,6 +231,53 @@ mod module
 	}
 }
 
+#[duplicate_item(directedness; [Directed]; [Undirected])]
+mod __
+{
+	use super::*;
+	use graphene::core::Ensure;
+
+	/// Tests `eccentricity_weighted`
+	#[quickcheck]
+	fn eccentricity_weighted(
+		Arb(g): Arb<VertexInGraph<ConnectedGraph<MockGraph<directedness>>>>,
+	) -> bool
+	{
+		let eccentricity = g.eccentricity_weighted(|w| w.value);
+		DijkstraShortestPaths::distances(&g, |w| w.value).all(|(_, dist)| dist <= eccentricity)
+	}
+
+	/// Tests `diameter_weighted`
+	#[quickcheck]
+	fn diameter_weighted(Arb(g): Arb<ConnectedGraph<MockGraph<directedness>>>) -> bool
+	{
+		let diameter = g.diameter_weighted(|w| w.value);
+		g.all_vertices().all(|v| {
+			VertexInGraph::ensure_unvalidated(&g, v).eccentricity_weighted(|w| w.value) <= diameter
+		})
+	}
+
+	/// Tests `radius_weighted`
+	#[quickcheck]
+	fn radius_weighted(Arb(g): Arb<ConnectedGraph<MockGraph<directedness>>>) -> bool
+	{
+		let radius = g.radius_weighted(|w| w.value);
+		g.all_vertices().all(|v| {
+			VertexInGraph::ensure_unvalidated(&g, v).eccentricity_weighted(|w| w.value) >= radius
+		})
+	}
+
+	/// Tests `centers_weighted`
+	#[quickcheck]
+	fn centers_weighted(Arb(g): Arb<ConnectedGraph<MockGraph<directedness>>>) -> bool
+	{
+		let radius = g.radius_weighted(|w| w.value);
+		g.centers_weighted(|w| w.value).all(|v| {
+			VertexInGraph::ensure_unvalidated(&g, v).eccentricity_weighted(|w| w.value) == radius
+		})
+	}
+}
+
 // Test that all Connected graphs are also unilateral and weak.
 assert_impl_all!(ConnectedGraph<MockGraph<MockDirectedness>>: Connected, Unilateral, Weak);