diff --git a/src/graph/graph_bind.cc b/src/graph/graph_bind.cc
index 3f1076da4360cae631e1bd08e52f75cd21c1003d..f440c630642be417e2afcbde845d23b21d87f906 100644
--- a/src/graph/graph_bind.cc
+++ b/src/graph/graph_bind.cc
@@ -576,4 +576,7 @@ BOOST_PYTHON_MODULE(libgraph_tool_core)
         .add_property("gcc_version", &LibInfo::GetGCCVersion);
 
     def("get_graph_type", &get_graph_type);
+
+    def("get_null_vertex",
+        +[](){ return graph_traits<GraphInterface::multigraph_t>::null_vertex();});
 }
diff --git a/src/graph/search/graph_bfs.cc b/src/graph/search/graph_bfs.cc
index ea34655c95e425addd55308e0d42f9329274b145..811b06a065722f7964dac63045439f128fc2e706 100644
--- a/src/graph/search/graph_bfs.cc
+++ b/src/graph/search/graph_bfs.cc
@@ -106,20 +106,28 @@ private:
     boost::python::object _vis;
 };
 
-struct do_bfs
-{
-    template <class Graph, class Visitor>
-    void operator()(Graph& g, size_t s, Visitor vis) const
-    {
-        breadth_first_search(g, vertex(s, g), visitor(vis));
-    }
-};
 
-void bfs_search(GraphInterface& g, size_t s, python::object vis)
+void bfs_search(GraphInterface& gi, size_t s, python::object vis)
 {
     run_action<graph_tool::all_graph_views,mpl::true_>()
-        (g, std::bind(do_bfs(), std::placeholders::_1, s,
-                      BFSVisitorWrapper(g, vis)))();
+        (gi,
+         [&](auto &g)
+         {
+             typedef typename std::remove_reference<decltype(g)>::type g_t;
+             typename vprop_map_t<default_color_type>::type
+                 color(get(vertex_index_t(), g));
+             auto visw = BFSVisitorWrapper(gi, vis);
+             auto v = vertex(s, g);
+             if (v == graph_traits<g_t>::null_vertex())
+             {
+                 for (auto u : vertices_range(g))
+                     breadth_first_search(g, u, visitor(visw).color_map(color));
+             }
+             else
+             {
+                 breadth_first_visit(g, v, visitor(visw).color_map(color));
+             }
+         })();
 }
 
 #ifdef HAVE_BOOST_COROUTINE
@@ -152,7 +160,28 @@ boost::python::object bfs_search_generator(GraphInterface& g, size_t s)
         {
             BFSGeneratorVisitor vis(g, yield);
             run_action<graph_tool::all_graph_views,mpl::true_>()
-                (g, std::bind(do_bfs(), std::placeholders::_1, s, vis))();
+                (g,
+                 [&](auto &g)
+                 {
+                     typedef typename std::remove_reference<decltype(g)>::type g_t;
+                     typename vprop_map_t<default_color_type>::type
+                         color(get(vertex_index_t(), g));
+
+                     auto v = vertex(s, g);
+                     if (v == graph_traits<g_t>::null_vertex())
+                     {
+                         for (auto u : vertices_range(g))
+                         {
+                             if (color[u] == color_traits<default_color_type>::black())
+                                 continue;
+                             breadth_first_visit(g, u, visitor(vis).color_map(color));
+                         }
+                     }
+                     else
+                     {
+                         breadth_first_visit(g, v, visitor(vis).color_map(color));
+                     }
+                 })();
         };
     return boost::python::object(CoroGenerator(dispatch));
 #else
diff --git a/src/graph/search/graph_dfs.cc b/src/graph/search/graph_dfs.cc
index a63921368927d3b4bbe3cccb15f341524f571ac4..439929cda4718204c8d3f3ea83505d13f06fe720 100644
--- a/src/graph/search/graph_dfs.cc
+++ b/src/graph/search/graph_dfs.cc
@@ -90,25 +90,22 @@ private:
     python::object _vis;
 };
 
-struct do_dfs
+void dfs_search(GraphInterface& gi, size_t s, python::object vis)
 {
-    template <class Graph, class VertexIndexMap, class Visitor>
-    void operator()(Graph& g, VertexIndexMap vertex_index, size_t s,
-                    Visitor vis) const
-    {
-        typename property_map_type::apply<default_color_type,
-                                          VertexIndexMap>::type
-            color(vertex_index);
-        depth_first_visit(g, vertex(s, g), vis, color);
-    }
-};
-
-
-void dfs_search(GraphInterface& g, size_t s, python::object vis)
-{
-    run_action<graph_tool::all_graph_views,mpl::true_>()
-        (g, std::bind(do_dfs(), std::placeholders::_1, g.get_vertex_index(),
-                      s, DFSVisitorWrapper(g, vis)))();
+    run_action<graph_tool::all_graph_views, mpl::true_>()
+        (gi,
+         [&](auto &g)
+         {
+             typedef typename std::remove_reference<decltype(g)>::type g_t;
+             typename vprop_map_t<default_color_type>::type
+                 color(get(vertex_index_t(), g));
+             auto visw = DFSVisitorWrapper(gi, vis);
+             auto v = vertex(s, g);
+             if (v == graph_traits<g_t>::null_vertex())
+                 depth_first_search(g, visw, color);
+             else
+                 depth_first_visit(g, v, visw, color);
+         })();
 }
 
 #ifdef HAVE_BOOST_COROUTINE
@@ -142,8 +139,18 @@ boost::python::object dfs_search_generator(GraphInterface& g, size_t s)
         {
             DFSGeneratorVisitor vis(g, yield);
             run_action<graph_tool::all_graph_views,mpl::true_>()
-                (g, std::bind(do_dfs(), std::placeholders::_1,
-                              g.get_vertex_index(), s, vis))();
+                (g,
+                 [&](auto &g)
+                 {
+                     typedef typename std::remove_reference<decltype(g)>::type g_t;
+                     typename vprop_map_t<default_color_type>::type
+                         color(get(vertex_index_t(), g));
+                     auto v = vertex(s, g);
+                     if (v == graph_traits<g_t>::null_vertex())
+                         depth_first_search(g, vis, color);
+                     else
+                         depth_first_visit(g, v, vis, color);
+                 })();
         };
     return boost::python::object(CoroGenerator(dispatch));
 #else
diff --git a/src/graph/search/graph_dijkstra.cc b/src/graph/search/graph_dijkstra.cc
index 58356044000575099e8e3ea214a3f303abdbf814..898c07514c27639e591e069001d9a33c69c3c969 100644
--- a/src/graph/search/graph_dijkstra.cc
+++ b/src/graph/search/graph_dijkstra.cc
@@ -140,11 +140,33 @@ struct do_djk_search
         typedef typename graph_traits<Graph>::edge_descriptor edge_t;
         DynamicPropertyMapWrap<dtype_t, edge_t> weight(aweight,
                                                        edge_properties());
-        dijkstra_shortest_paths_no_color_map
-            (g, vertex(s, g), visitor(vis).weight_map(weight).
-             predecessor_map(pred_map).
-             distance_map(dist).distance_compare(cmp).
-             distance_combine(cmb).distance_inf(i).distance_zero(z));
+
+        if (vertex(s, g) == graph_traits<Graph>::null_vertex())
+        {
+            for (auto u : vertices_range(g))
+            {
+                vis.initialize_vertex(u, g);
+                put(dist, u, i);
+                put(pred_map, u, u);
+            }
+            for (auto u : vertices_range(g))
+            {
+                if (dist[u] != i)
+                    continue;
+                dist[u] = z;
+                dijkstra_shortest_paths_no_color_map_no_init
+                    (g, u, pred_map, dist, weight, get(vertex_index_t(), g),
+                     cmp, cmb, i, z, vis);
+            }
+        }
+        else
+        {
+            dijkstra_shortest_paths_no_color_map
+                (g, vertex(s, g), visitor(vis).weight_map(weight).
+                 predecessor_map(pred_map).
+                 distance_map(dist).distance_compare(cmp).
+                 distance_combine(cmb).distance_inf(i).distance_zero(z));
+        }
     }
 };
 
@@ -158,9 +180,31 @@ struct do_djk_search_fast
         typedef typename property_traits<DistanceMap>::value_type dtype_t;
         dtype_t z = python::extract<dtype_t>(range.first);
         dtype_t i = python::extract<dtype_t>(range.second);
-        dijkstra_shortest_paths_no_color_map
-            (g, vertex(s, g), visitor(vis).weight_map(weight).
-             distance_map(dist).distance_inf(i).distance_zero(z));
+
+        if (vertex(s, g) == graph_traits<Graph>::null_vertex())
+        {
+            for (auto u : vertices_range(g))
+            {
+                vis.initialize_vertex(u, g);
+                put(dist, u, i);
+            }
+            for (auto u : vertices_range(g))
+            {
+                if (dist[u] != i)
+                    continue;
+                dist[u] = z;
+                dijkstra_shortest_paths_no_color_map_no_init
+                    (g, u, dummy_property_map(), dist, weight,
+                     get(vertex_index_t(), g), std::less<dtype_t>(),
+                     boost::closed_plus<dtype_t>(), i, z, vis);
+            }
+        }
+        else
+        {
+            dijkstra_shortest_paths_no_color_map
+                (g, vertex(s, g), visitor(vis).weight_map(weight).
+                 distance_map(dist).distance_inf(i).distance_zero(z));
+        }
     }
 };
 
diff --git a/src/graph_tool/__init__.py b/src/graph_tool/__init__.py
index 13d48621d4692a6cba785e47e1d9062fc5b4af02..bbd5cd60915878d453b97b8818d7c987418ad428 100644
--- a/src/graph_tool/__init__.py
+++ b/src/graph_tool/__init__.py
@@ -3261,6 +3261,7 @@ VertexBase.is_valid = Vertex.is_valid
 Vertex = VertexBase
 Vertex.__name__ = "Vertex"
 
+_get_null_vertex = libcore.get_null_vertex
 
 # Add convenience function to vector classes
 def _get_array_view(self):
diff --git a/src/graph_tool/search/__init__.py b/src/graph_tool/search/__init__.py
index 6977511cbc08803ac7ff1012d18d5f6142da0715..0291a9fe25a09423e8ede90ce8e798fd446ad002 100644
--- a/src/graph_tool/search/__init__.py
+++ b/src/graph_tool/search/__init__.py
@@ -92,7 +92,7 @@ if sys.version_info < (3,):
 from .. dl_import import dl_import
 dl_import("from . import libgraph_tool_search")
 
-from .. import _prop, _python_type
+from .. import _prop, _python_type, _get_null_vertex
 import weakref
 import numpy
 
@@ -157,15 +157,17 @@ class BFSVisitor(object):
         return
 
 
-def bfs_search(g, source, visitor=BFSVisitor()):
+def bfs_search(g, source=None, visitor=BFSVisitor()):
     r"""Breadth-first traversal of a directed or undirected graph.
 
     Parameters
     ----------
     g : :class:`~graph_tool.Graph`
         Graph to be used.
-    source : :class:`~graph_tool.Vertex`
-        Source vertex.
+    source : :class:`~graph_tool.Vertex` (optional, default: ``None``)
+        Source vertex. If unspecified, all vertices will be traversed, by
+        iterating over starting vertices according to their index in increasing
+        order.
     visitor : :class:`~graph_tool.search.BFSVisitor` (optional, default: ``BFSVisitor()``)
         A visitor object that is invoked at the event points inside the
         algorithm. This should be a subclass of
@@ -284,12 +286,16 @@ def bfs_search(g, source, visitor=BFSVisitor()):
     """
 
     try:
+        if source is None:
+            source = _get_null_vertex()
+        else:
+            source = int(source)
         libgraph_tool_search.bfs_search(g._Graph__graph,
-                                        int(source), visitor)
+                                        source, visitor)
     except StopSearch:
         pass
 
-def bfs_iterator(g, source):
+def bfs_iterator(g, source=None):
     r"""Return an iterator of the edges corresponding to a breath-first traversal of
     the graph.
 
@@ -297,8 +303,10 @@ def bfs_iterator(g, source):
     ----------
     g : :class:`~graph_tool.Graph`
         Graph to be used.
-    source : :class:`~graph_tool.Vertex`
-        Source vertex.
+    source : :class:`~graph_tool.Vertex` (optional, default: ``None``)
+        Source vertex. If unspecified, all vertices will be traversed, by
+        iterating over starting vertices according to their index in increasing
+        order.
 
     Returns
     -------
@@ -341,8 +349,11 @@ def bfs_iterator(g, source):
     .. [bfs-bgl] http://www.boost.org/doc/libs/release/libs/graph/doc/breadth_first_search.html
     .. [bfs-wikipedia] http://en.wikipedia.org/wiki/Breadth-first_search
     """
-
-    return libgraph_tool_search.bfs_search_generator(g._Graph__graph, int(source))
+    if source is None:
+        source = _get_null_vertex()
+    else:
+        source = int(source)
+    return libgraph_tool_search.bfs_search_generator(g._Graph__graph, source)
 
 
 class DFSVisitor(object):
@@ -415,15 +426,17 @@ class DFSVisitor(object):
         return
 
 
-def dfs_search(g, source, visitor=DFSVisitor()):
+def dfs_search(g, source=None, visitor=DFSVisitor()):
     r"""Depth-first traversal of a directed or undirected graph.
 
     Parameters
     ----------
     g : :class:`~graph_tool.Graph`
         Graph to be used.
-    source : :class:`~graph_tool.Vertex`
-        Source vertex.
+    source : :class:`~graph_tool.Vertex` (optional, default: ``None``)
+        Source vertex. If unspecified, all vertices will be traversed, by
+        iterating over starting vertices according to their index in increasing
+        order.
     visitor : :class:`~graph_tool.search.DFSVisitor` (optional, default: ``DFSVisitor()``)
         A visitor object that is invoked at the event points inside the
         algorithm. This should be a subclass of
@@ -563,15 +576,20 @@ def dfs_search(g, source, visitor=DFSVisitor()):
     ----------
     .. [dfs-bgl] http://www.boost.org/doc/libs/release/libs/graph/doc/depth_first_search.html
     .. [dfs-wikipedia] http://en.wikipedia.org/wiki/Depth-first_search
+
     """
 
     try:
+        if source is None:
+            source = _get_null_vertex()
+        else:
+            source = int(source)
         libgraph_tool_search.dfs_search(g._Graph__graph,
-                                        int(source), visitor)
+                                        source, visitor)
     except StopSearch:
         pass
 
-def dfs_iterator(g, source):
+def dfs_iterator(g, source=None):
     r"""Return an iterator of the edges corresponding to a depth-first traversal of
     the graph.
 
@@ -579,8 +597,10 @@ def dfs_iterator(g, source):
     ----------
     g : :class:`~graph_tool.Graph`
         Graph to be used.
-    source : :class:`~graph_tool.Vertex`
-        Source vertex.
+    source : :class:`~graph_tool.Vertex` (optional, default: ``None``)
+        Source vertex. If unspecified, all vertices will be traversed, by
+        iterating over starting vertices according to their index in increasing
+        order.
 
     Returns
     -------
@@ -622,7 +642,11 @@ def dfs_iterator(g, source):
     .. [dfs-wikipedia] http://en.wikipedia.org/wiki/Depth-first_search
     """
 
-    return libgraph_tool_search.dfs_search_generator(g._Graph__graph, int(source))
+    if source is None:
+        source = _get_null_vertex()
+    else:
+        source = int(source)
+    return libgraph_tool_search.dfs_search_generator(g._Graph__graph, source)
 
 class DijkstraVisitor(object):
     r"""A visitor object that is invoked at the event-points inside the
@@ -686,7 +710,7 @@ class DijkstraVisitor(object):
         return
 
 
-def dijkstra_search(g, source, weight, visitor=DijkstraVisitor(), dist_map=None,
+def dijkstra_search(g, weight, source=None, visitor=DijkstraVisitor(), dist_map=None,
                     pred_map=None, combine=lambda a, b: a + b,
                     compare=lambda a, b: a < b, zero=0, infinity=numpy.inf):
     r"""Dijsktra traversal of a directed or undirected graph, with non-negative weights.
@@ -695,10 +719,12 @@ def dijkstra_search(g, source, weight, visitor=DijkstraVisitor(), dist_map=None,
     ----------
     g : :class:`~graph_tool.Graph`
         Graph to be used.
-    source : :class:`~graph_tool.Vertex`
-        Source vertex.
     weight : :class:`~graph_tool.PropertyMap`
         Edge property map with weight values.
+    source : :class:`~graph_tool.Vertex` (optional, default: ``None``)
+        Source vertex. If unspecified, all vertices will be traversed, by
+        iterating over starting vertices according to their index in increasing
+        order.
     visitor : :class:`~graph_tool.search.DijkstraVisitor` (optional, default: ``DijkstraVisitor()``)
         A visitor object that is invoked at the event points inside the
         algorithm. This should be a subclass of
@@ -815,7 +841,7 @@ def dijkstra_search(g, source, weight, visitor=DijkstraVisitor(), dist_map=None,
     With the above class defined, we can perform the Dijkstra search as follows.
 
     >>> time = g.new_vertex_property("int")
-    >>> dist, pred = gt.dijkstra_search(g, g.vertex(0), weight, VisitorExample(name, time))
+    >>> dist, pred = gt.dijkstra_search(g, weight, g.vertex(0), VisitorExample(name, time))
     --> Bob has been discovered!
     edge (Bob, Eve) has been examined...
     edge (Bob, Eve) has been relaxed...
@@ -910,8 +936,12 @@ def dijkstra_search(g, source, weight, visitor=DijkstraVisitor(), dist_map=None,
         infinity = _python_type(dist_map.value_type())(infinity)
 
     try:
+        if source is None:
+            source = _get_null_vertex()
+        else:
+            source = int(source)
         libgraph_tool_search.dijkstra_search(g._Graph__graph,
-                                             int(source),
+                                             source,
                                              _prop("v", g, dist_map),
                                              _prop("v", g, pred_map),
                                              _prop("e", g, weight), visitor,
@@ -921,7 +951,7 @@ def dijkstra_search(g, source, weight, visitor=DijkstraVisitor(), dist_map=None,
 
     return dist_map, pred_map
 
-def dijkstra_iterator(g, source, weight, dist_map=None, combine=None,
+def dijkstra_iterator(g, weight, source=None, dist_map=None, combine=None,
                       compare=None, zero=0, infinity=numpy.inf):
     r"""Return an iterator of the edges corresponding to a Dijkstra traversal of
     the graph.
@@ -930,10 +960,12 @@ def dijkstra_iterator(g, source, weight, dist_map=None, combine=None,
     ----------
     g : :class:`~graph_tool.Graph`
         Graph to be used.
-    source : :class:`~graph_tool.Vertex`
-        Source vertex.
     weight : :class:`~graph_tool.PropertyMap`
         Edge property map with weight values.
+    source : :class:`~graph_tool.Vertex` (optional, default: ``None``)
+        Source vertex. If unspecified, all vertices will be traversed, by
+        iterating over starting vertices according to their index in increasing
+        order.
     dist_map : :class:`~graph_tool.PropertyMap` (optional, default: ``None``)
         A vertex property map where the distances from the source will be
         stored.
@@ -972,7 +1004,7 @@ def dijkstra_iterator(g, source, weight, dist_map=None, combine=None,
     Examples
     --------
 
-    >>> for e in gt.dijkstra_iterator(g, g.vertex(0), weight):
+    >>> for e in gt.dijkstra_iterator(g, weight, g.vertex(0)):
     ...    print(name[e.source()], "->", name[e.target()])
     Bob -> Eve
     Bob -> Chuck
@@ -1009,9 +1041,13 @@ def dijkstra_iterator(g, source, weight, dist_map=None, combine=None,
         infinity = (weight.a.max() + 1) * g.num_vertices()
         infinity = _python_type(dist_map.value_type())(infinity)
 
+    if source is None:
+        source = _get_null_vertex()
+    else:
+        source = int(source)
     if compare is None and combine is None:
         return libgraph_tool_search.dijkstra_generator_fast(g._Graph__graph,
-                                                            int(source),
+                                                            source,
                                                             _prop("v", g, dist_map),
                                                             _prop("e", g, weight),
                                                             zero, infinity)
@@ -1021,7 +1057,7 @@ def dijkstra_iterator(g, source, weight, dist_map=None, combine=None,
         if combine is None:
             combine = lambda a, b: a + b
         return libgraph_tool_search.dijkstra_generator(g._Graph__graph,
-                                                       int(source),
+                                                       source,
                                                        _prop("v", g, dist_map),
                                                        _prop("e", g, weight),
                                                        compare, combine,