diff --git a/include/boost/graph/connected_components.hpp b/include/boost/graph/connected_components.hpp
index 0e98512d0..89b301075 100644
--- a/include/boost/graph/connected_components.hpp
+++ b/include/boost/graph/connected_components.hpp
@@ -69,8 +69,12 @@ connected_components(const Graph& g, ComponentMap c,
     const bgl_named_params< P, T, R >& params BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
         Graph, vertex_list_graph_tag))
 {
-    if (num_vertices(g) == 0)
+    // num_vertices also counts the vertices hidden by a filtered_graph
+    const auto vertex_range = vertices(g);
+    if (vertex_range.first == vertex_range.second)
+    {
         return 0;
+    }
 
     typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
     BOOST_CONCEPT_ASSERT((WritablePropertyMapConcept< ComponentMap, Vertex >));
@@ -91,8 +95,12 @@ connected_components(const Graph& g,
     ComponentMap c BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
         Graph, vertex_list_graph_tag))
 {
-    if (num_vertices(g) == 0)
+    // num_vertices also counts the vertices hidden by a filtered_graph
+    const auto vertex_range = vertices(g);
+    if (vertex_range.first == vertex_range.second)
+    {
         return 0;
+    }
 
     typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
     BOOST_CONCEPT_ASSERT((WritablePropertyMapConcept< ComponentMap, Vertex >));
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index acb9b6bbf..156872d4f 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -128,6 +128,7 @@ alias graph_test_regular :
     [ run floyd_warshall_test.cpp ]
     [ run astar_search_test.cpp ]
     [ run biconnected_components_test.cpp ]
+    [ run connected_components_test.cpp ]
     [ run min_degree_empty.cpp ]
     [ run cuthill_mckee_ordering.cpp ]
     [ run king_ordering.cpp ]
diff --git a/test/connected_components_test.cpp b/test/connected_components_test.cpp
new file mode 100644
index 000000000..e41dbdb2f
--- /dev/null
+++ b/test/connected_components_test.cpp
@@ -0,0 +1,44 @@
+//=======================================================================
+// Copyright (c) 2026 Arnaud Becheler
+//
+// Distributed under the Boost Software License, Version 1.0. (See
+// accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+//=======================================================================
+
+#include <boost/graph/connected_components.hpp>
+#include <boost/core/lightweight_test.hpp>
+#include <boost/graph/adjacency_list.hpp>
+#include <boost/graph/filtered_graph.hpp>
+#include <boost/property_map/property_map.hpp>
+#include <vector>
+
+using Graph = ::boost::adjacency_list< ::boost::vecS, ::boost::vecS, ::boost::undirectedS >;
+using Vertex = ::boost::graph_traits< Graph >::vertex_descriptor;
+
+// Hides every vertex.
+struct keep_none
+{
+    bool operator()(Vertex) const { return false; }
+};
+
+using FilteredGraph = ::boost::filtered_graph< Graph, ::boost::keep_all, keep_none >;
+
+// Checks that a filtered graph with no visible vertex has no components.
+void test_all_vertices_filtered_out()
+{
+    const Graph base(3);
+    const FilteredGraph g(base, ::boost::keep_all(), keep_none());
+
+    std::vector< int > component_vec(::boost::num_vertices(g), -1);
+    auto component_map = ::boost::make_iterator_property_map(component_vec.begin(), ::boost::get(::boost::vertex_index, g));
+    const int num_components = ::boost::connected_components(g, component_map);
+
+    BOOST_TEST_EQ(num_components, 0);
+}
+
+int main()
+{
+    test_all_vertices_filtered_out();
+    return ::boost::report_errors();
+}