Change path graph size parameter by 1, add doc link and P(n) notation

src/generators.rs

@@ -46,16 +46,19 @@ where
 
 /// Generates a path graph.
 ///
-/// Generates a path with `n` edges in `graph` as a new connected component and returns the new
+/// Generates a [path graph] *P(n)* with `n` vertices and `n - 1` edges in `graph` as a new
-/// vertices *v0, v1, ..., vn* and edges *e0, e1, ..., e(n - 1)* in order, i.e. *e0 = (v0, v1)*,
+/// connected component and returns the new vertices *v0, v1, ..., v(n - 1)* and edges
-/// *e1 = (v1, v2)*, etc.
+/// *e0, e1, ..., e(n - 2)* in order, i.e. *e0 = (v0, v1)*, *e1 = (v1, v2)*, etc. and *v0* and
+/// *v(n-1)* being the two terminal vertices
 ///
-/// For `n == 0`, only a single vertex and no edges are added.
+/// For `n == 0`, nothing is added. For `n == 1`, only a single vertex and no edges are added.
+///
+/// [Path graph]: https://en.wikipedia.org/wiki/Path_graph
 pub fn path<G: GraphTopologyAddition>(graph: &mut G, n: usize) -> (Vec<G::Vertex>, Vec<G::Edge>) {
-    graph.reserve_vertices(n + 1);
+    graph.reserve_vertices(n);
-    graph.reserve_edges(n);
+    graph.reserve_edges(n - 1);
-    let vertices: Vec<_> = (0..n + 1).map(|_| graph.add_vertex()).collect();
+    let vertices: Vec<_> = (0..n).map(|_| graph.add_vertex()).collect();
-    let edges = (0..n)
+    let edges = (0..n - 1)
         .map(|i| graph.add_edge(vertices[i], vertices[i + 1]))
         .collect();
     (vertices, edges)