diff --git a/src/undirected/connected_components.rs b/src/undirected/connected_components.rs
index 7526ffc2..50d27086 100644
--- a/src/undirected/connected_components.rs
+++ b/src/undirected/connected_components.rs
@@ -124,18 +124,24 @@ where
 
     /// Extract connected components from a graph.
     ///
-    /// - `starts` is a collection of vertices to be considered as start points.
+    /// - `candidates` is the collection of candidate vertices whose neighbour
+    ///   groups should be merged into connected components.
     /// - `neighbours` is a function returning the neighbours of a given node.
     ///
+    /// Only the candidate vertices are queried with `neighbours`. Vertices
+    /// returned by `neighbours` are added to their candidate vertex group, but
+    /// their own neighbours are not explored unless they also appear in
+    /// `candidates`.
+    ///
     /// This function returns a list of sets of nodes forming disjoint connected
     /// sets.
-    pub fn connected_components<FN, IN>(starts: &[N], mut neighbours: FN) -> C2
+    pub fn connected_components<FN, IN>(candidates: &[N], mut neighbours: FN) -> C2
     where
         FN: FnMut(&N) -> IN,
         IN: IntoIterator<Item = N>,
     {
         ConnectedComponents::<N, Vec<N>, It2, C1, C2, C3>::components(
-            &starts
+            &candidates
                 .iter()
                 .map(|s| {
                     neighbours(s)
@@ -216,18 +222,24 @@ where
 
 /// Extract connected components from a graph.
 ///
-/// - `starts` is a collection of vertices to be considered as start points.
+/// - `candidates` is the collection of candidate vertices whose neighbour
+///   groups should be merged into connected components.
 /// - `neighbours` is a function returning the neighbours of a given node.
 ///
+/// Only the candidate vertices are queried with `neighbours`. Vertices
+/// returned by `neighbours` are added to their candidate vertex group, but
+/// their own neighbours are not explored unless they also appear in
+/// `candidates`.
+///
 /// This function returns a list of sets of nodes forming disjoint connected
 /// sets.
-pub fn connected_components<N, FN, IN>(starts: &[N], neighbours: FN) -> Vec<HashSet<N>>
+pub fn connected_components<N, FN, IN>(candidates: &[N], neighbours: FN) -> Vec<HashSet<N>>
 where
     N: Clone + Hash + Eq,
     FN: FnMut(&N) -> IN,
     IN: IntoIterator<Item = N>,
 {
-    ConnectedComponents::<N>::connected_components(starts, neighbours)
+    ConnectedComponents::<N>::connected_components(candidates, neighbours)
 }
 
 /// Locate vertices amongst disjoint sets.
diff --git a/tests/connected-components.rs b/tests/connected-components.rs
index d230b02c..2cd95dfe 100644
--- a/tests/connected-components.rs
+++ b/tests/connected-components.rs
@@ -55,7 +55,7 @@ fn empty_components() {
 }
 
 #[test]
-fn basic_connected_components() {
+fn connected_components_only_queries_candidate_vertices() {
     let mut counter = 0;
     let mut c = connected_components(&[1, 4], |&n| {
         counter += 1;
@@ -75,6 +75,7 @@ fn basic_connected_components() {
         c[1].clone().into_iter().sorted().collect_vec(),
         vec![2, 4, 6, 8]
     );
+    // Only the candidate vertices are queried for neighbours.
     assert_eq!(counter, 2);
 }